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\subsection{Fizhi: High-end Atmospheric Physics} |
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\label{sec:pkg:fizhi} |
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\begin{rawhtml} |
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<!-- CMIREDIR:package_fizhi: --> |
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\end{rawhtml} |
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\input{texinputs/epsf.tex} |
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|
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\subsubsection{Introduction} |
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The fizhi (high-end atmospheric physics) package includes a collection of state-of-the-art |
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physical parameterizations for atmospheric radiation, cumulus convection, atmospheric |
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boundary layer turbulence, and land surface processes. The collection of atmospheric |
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physics parameterizations were originally used together as part of the GEOS-3 |
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(Goddard Earth Observing System-3) GCM developed at the NASA/Goddard Global Modelling |
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and Assimilation Office (GMAO). |
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1.1 |
|
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% ************************************************************************* |
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% ************************************************************************* |
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1.9 |
\subsubsection{Equations} |
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1.1 |
|
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1.9 |
Moist Convective Processes: |
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|
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\paragraph{Sub-grid and Large-scale Convection} |
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\label{sec:fizhi:mc} |
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Sub-grid scale cumulus convection is parameterized using the Relaxed Arakawa |
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Schubert (RAS) scheme of \cite{moorsz:92}, which is a linearized Arakawa Schubert |
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1.1 |
type scheme. RAS predicts the mass flux from an ensemble of clouds. Each subensemble is identified |
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by its entrainment rate and level of neutral bouyancy which are determined by the grid-scale properties. |
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The thermodynamic variables that are used in RAS to describe the grid scale vertical profile are |
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the dry static energy, $s=c_pT +gz$, and the moist static energy, $h=c_p T + gz + Lq$. |
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The conceptual model behind RAS depicts each subensemble as a rising plume cloud, entraining |
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mass from the environment during ascent, and detraining all cloud air at the level of neutral |
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buoyancy. RAS assumes that the normalized cloud mass flux, $\eta$, normalized by the cloud base |
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mass flux, is a linear function of height, expressed as: |
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\[ |
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\pp{\eta(z)}{z} = \lambda \hspace{0.4cm}or\hspace{0.4cm} \pp{\eta(P^{\kappa})}{P^{\kappa}} = |
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-{c_p \over {g}}\theta\lambda |
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\] |
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where we have used the hydrostatic equation written in the form: |
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\[ |
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\pp{z}{P^{\kappa}} = -{c_p \over {g}}\theta |
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\] |
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The entrainment parameter, $\lambda$, characterizes a particular subensemble based on its |
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detrainment level, and is obtained by assuming that the level of detrainment is the level of neutral |
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buoyancy, ie., the level at which the moist static energy of the cloud, $h_c$, is equal |
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1.10 |
to the saturation moist static energy of the environment, $h^*$. Following \cite{moorsz:92}, |
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1.1 |
$\lambda$ may be written as |
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\[ |
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\lambda = { {h_B - h^*_D} \over { {c_p \over g} {\int_{P_D}^{P_B}\theta(h^*_D-h)dP^{\kappa}}} } , |
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\] |
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where the subscript $B$ refers to cloud base, and the subscript $D$ refers to the detrainment level. |
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The convective instability is measured in terms of the cloud work function $A$, defined as the |
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rate of change of cumulus kinetic energy. The cloud work function is |
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related to the buoyancy, or the difference |
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between the moist static energy in the cloud and in the environment: |
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\[ |
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A = \int_{P_D}^{P_B} { {\eta \over {1 + \gamma} } |
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\left[ {{h_c-h^*} \over {P^{\kappa}}} \right] dP^{\kappa}} |
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\] |
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where $\gamma$ is ${L \over {c_p}}\pp{q^*}{T}$ obtained from the Claussius Clapeyron equation, |
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and the subscript $c$ refers to the value inside the cloud. |
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To determine the cloud base mass flux, the rate of change of $A$ in time {\em due to dissipation by |
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the clouds} is assumed to approximately balance the rate of change of $A$ {\em due to the generation |
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by the large scale}. This is the quasi-equilibrium assumption, and results in an expression for $m_B$: |
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\[ |
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m_B = {{- \left.{dA \over dt} \right|_{ls}} \over K} |
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\] |
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where $K$ is the cloud kernel, defined as the rate of change of the cloud work function per |
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unit cloud base mass flux, and is currently obtained by analytically differentiating the |
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expression for $A$ in time. |
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The rate of change of $A$ due to the generation by the large scale can be written as the |
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difference between the current $A(t+\Delta t)$ and its equillibrated value after the previous |
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convective time step |
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$A(t)$, divided by the time step. $A(t)$ is approximated as some critical $A_{crit}$, |
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computed by Lord (1982) from $in situ$ observations. |
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The predicted convective mass fluxes are used to solve grid-scale temperature |
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and moisture budget equations to determine the impact of convection on the large scale fields of |
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temperature (through latent heating and compensating subsidence) and moisture (through |
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precipitation and detrainment): |
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\[ |
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\left.{\pp{\theta}{t}}\right|_{c} = \alpha { m_B \over {c_p P^{\kappa}}} \eta \pp{s}{p} |
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\] |
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and |
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\[ |
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\left.{\pp{q}{t}}\right|_{c} = \alpha { m_B \over {L}} \eta (\pp{h}{p}-\pp{s}{p}) |
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\] |
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where $\theta = {T \over P^{\kappa}}$, $P = (p/p_0)$, and $\alpha$ is the relaxation parameter. |
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As an approximation to a full interaction between the different allowable subensembles, |
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many clouds are simulated frequently, each modifying the large scale environment some fraction |
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$\alpha$ of the total adjustment. The parameterization thereby ``relaxes'' the large scale environment |
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towards equillibrium. |
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In addition to the RAS cumulus convection scheme, the fizhi package employs a |
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Kessler-type scheme for the re-evaporation of falling rain (\cite{sudm:88}), which |
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1.1 |
correspondingly adjusts the temperature assuming $h$ is conserved. RAS in its current |
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formulation assumes that all cloud water is deposited into the detrainment level as rain. |
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All of the rain is available for re-evaporation, which begins in the level below detrainment. |
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The scheme accounts for some microphysics such as |
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the rainfall intensity, the drop size distribution, as well as the temperature, |
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pressure and relative humidity of the surrounding air. The fraction of the moisture deficit |
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in any model layer into which the rain may re-evaporate is controlled by a free parameter, |
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which allows for a relatively efficient re-evaporation of liquid precipitate and larger rainout |
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for frozen precipitation. |
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Due to the increased vertical resolution near the surface, the lowest model |
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layers are averaged to provide a 50 mb thick sub-cloud layer for RAS. Each time RAS is |
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invoked (every ten simulated minutes), |
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a number of randomly chosen subensembles are checked for the possibility |
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of convection, from just above cloud base to 10 mb. |
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Supersaturation or large-scale precipitation is initiated in the fizhi package whenever |
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the relative humidity in any grid-box exceeds a critical value, currently 100 \%. |
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The large-scale precipitation re-evaporates during descent to partially saturate |
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lower layers in a process identical to the re-evaporation of convective rain. |
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1.5 |
\paragraph{Cloud Formation} |
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1.1 |
\label{sec:fizhi:clouds} |
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Convective and large-scale cloud fractons which are used for cloud-radiative interactions are determined |
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diagnostically as part of the cumulus and large-scale parameterizations. |
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Convective cloud fractions produced by RAS are proportional to the |
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detrained liquid water amount given by |
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\[ |
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F_{RAS} = \min\left[ {l_{RAS}\over l_c}, 1.0 \right] |
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\] |
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where $l_c$ is an assigned critical value equal to $1.25$ g/kg. |
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A memory is associated with convective clouds defined by: |
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\[ |
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F_{RAS}^n = \min\left[ F_{RAS} + (1-{\Delta t_{RAS}\over\tau})F_{RAS}^{n-1}, 1.0 \right] |
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\] |
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where $F_{RAS}$ is the instantanious cloud fraction and $F_{RAS}^{n-1}$ is the cloud fraction |
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from the previous RAS timestep. The memory coefficient is computed using a RAS cloud timescale, |
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$\tau$, equal to 1 hour. RAS cloud fractions are cleared when they fall below 5 \%. |
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Large-scale cloudiness is defined, following Slingo and Ritter (1985), as a function of relative |
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humidity: |
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\[ |
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F_{LS} = \min\left[ { \left( {RH-RH_c \over 1-RH_c} \right) }^2, 1.0 \right] |
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\] |
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|
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where |
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\bqa |
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RH_c & = & 1-s(1-s)(2-\sqrt{3}+2\sqrt{3} \, s)r \nonumber \\ |
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s & = & p/p_{surf} \nonumber \\ |
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r & = & \left( {1.0-RH_{min} \over \alpha} \right) \nonumber \\ |
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RH_{min} & = & 0.75 \nonumber \\ |
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\alpha & = & 0.573285 \nonumber . |
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\eqa |
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These cloud fractions are suppressed, however, in regions where the convective |
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sub-cloud layer is conditionally unstable. The functional form of $RH_c$ is shown in |
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1.13 |
Figure (\ref{fig.rhcrit}). |
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1.1 |
|
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\begin{figure*}[htbp] |
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\vspace{0.4in} |
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1.4 |
\centerline{ \epsfysize=4.0in \epsfbox{part6/rhcrit.ps}} |
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1.1 |
\vspace{0.4in} |
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1.13 |
\caption [Critical Relative Humidity for Clouds.] |
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{Critical Relative Humidity for Clouds.} |
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\label{fig.rhcrit} |
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molod |
1.1 |
\end{figure*} |
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The total cloud fraction in a grid box is determined by the larger of the two cloud fractions: |
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\[ |
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F_{CLD} = \max \left[ F_{RAS},F_{LS} \right] . |
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\] |
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Finally, cloud fractions are time-averaged between calls to the radiation packages. |
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molod |
1.9 |
Radiation: |
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1.1 |
|
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The parameterization of radiative heating in the fizhi package includes effects |
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from both shortwave and longwave processes. |
196 |
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Radiative fluxes are calculated at each |
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model edge-level in both up and down directions. |
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The heating rates/cooling rates are then obtained |
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from the vertical divergence of the net radiative fluxes. |
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The net flux is |
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\[ |
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F = F^\uparrow - F^\downarrow |
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\] |
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where $F$ is the net flux, $F^\uparrow$ is the upward flux and $F^\downarrow$ is |
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the downward flux. |
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The heating rate due to the divergence of the radiative flux is given by |
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\[ |
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\pp{\rho c_p T}{t} = - \pp{F}{z} |
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\] |
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or |
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\[ |
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\pp{T}{t} = \frac{g}{c_p \pi} \pp{F}{\sigma} |
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\] |
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where $g$ is the accelation due to gravity |
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and $c_p$ is the heat capacity of air at constant pressure. |
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The time tendency for Longwave |
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Radiation is updated every 3 hours. The time tendency for Shortwave Radiation is updated once |
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every three hours assuming a normalized incident solar radiation, and subsequently modified at |
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every model time step by the true incident radiation. |
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The solar constant value used in the package is equal to 1365 $W/m^2$ |
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and a $CO_2$ mixing ratio of 330 ppm. |
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For the ozone mixing ratio, monthly mean zonally averaged |
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climatological values specified as a function |
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1.10 |
of latitude and height (\cite{rosen:87}) are linearly interpolated to the current time. |
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1.1 |
|
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|
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1.5 |
\paragraph{Shortwave Radiation} |
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1.1 |
|
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The shortwave radiation package used in the package computes solar radiative |
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heating due to the absoption by water vapor, ozone, carbon dioxide, oxygen, |
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clouds, and aerosols and due to the |
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scattering by clouds, aerosols, and gases. |
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The shortwave radiative processes are described by |
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1.10 |
\cite{chou:90,chou:92}. This shortwave package |
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1.1 |
uses the Delta-Eddington approximation to compute the |
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bulk scattering properties of a single layer following King and Harshvardhan (JAS, 1986). |
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The transmittance and reflectance of diffuse radiation |
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molod |
1.10 |
follow the procedures of Sagan and Pollock (JGR, 1967) and \cite{lhans:74}. |
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molod |
1.1 |
|
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Highly accurate heating rate calculations are obtained through the use |
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of an optimal grouping strategy of spectral bands. By grouping the UV and visible regions |
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as indicated in Table \ref{tab:fizhi:solar2}, the Rayleigh scattering and the ozone absorption of solar radiation |
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can be accurately computed in the ultraviolet region and the photosynthetically |
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active radiation (PAR) region. |
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The computation of solar flux in the infrared region is performed with a broadband |
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parameterization using the spectrum regions shown in Table \ref{tab:fizhi:solar1}. |
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The solar radiation algorithm used in the fizhi package can be applied not only for climate studies but |
251 |
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also for studies on the photolysis in the upper atmosphere and the photosynthesis in the biosphere. |
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\begin{table}[htb] |
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\begin{center} |
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{\bf UV and Visible Spectral Regions} \\ |
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\vspace{0.1in} |
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\begin{tabular}{|c|c|c|} |
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\hline |
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Region & Band & Wavelength (micron) \\ \hline |
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\hline |
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UV-C & 1. & .175 - .225 \\ |
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& 2. & .225 - .245 \\ |
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& & .260 - .280 \\ |
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& 3. & .245 - .260 \\ \hline |
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UV-B & 4. & .280 - .295 \\ |
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& 5. & .295 - .310 \\ |
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& 6. & .310 - .320 \\ \hline |
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UV-A & 7. & .320 - .400 \\ \hline |
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PAR & 8. & .400 - .700 \\ |
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\hline |
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\end{tabular} |
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\end{center} |
273 |
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\caption{UV and Visible Spectral Regions used in shortwave radiation package.} |
274 |
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\label{tab:fizhi:solar2} |
275 |
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\end{table} |
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|
277 |
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\begin{table}[htb] |
278 |
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\begin{center} |
279 |
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{\bf Infrared Spectral Regions} \\ |
280 |
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\vspace{0.1in} |
281 |
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\begin{tabular}{|c|c|c|} |
282 |
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\hline |
283 |
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Band & Wavenumber(cm$^{-1}$) & Wavelength (micron) \\ \hline |
284 |
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\hline |
285 |
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1 & 1000-4400 & 2.27-10.0 \\ |
286 |
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2 & 4400-8200 & 1.22-2.27 \\ |
287 |
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3 & 8200-14300 & 0.70-1.22 \\ |
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\hline |
289 |
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\end{tabular} |
290 |
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\end{center} |
291 |
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\caption{Infrared Spectral Regions used in shortwave radiation package.} |
292 |
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\label{tab:fizhi:solar1} |
293 |
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\end{table} |
294 |
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Within the shortwave radiation package, |
296 |
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both ice and liquid cloud particles are allowed to co-exist in any of the model layers. |
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Two sets of cloud parameters are used, one for ice paticles and the other for liquid particles. |
298 |
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Cloud parameters are defined as the cloud optical thickness and the effective cloud particle size. |
299 |
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In the fizhi package, the effective radius for water droplets is given as 10 microns, |
300 |
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while 65 microns is used for ice particles. The absorption due to aerosols is currently |
301 |
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set to zero. |
302 |
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|
303 |
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To simplify calculations in a cloudy atmosphere, clouds are |
304 |
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grouped into low ($p>700$ mb), middle (700 mb $\ge p > 400$ mb), and high ($p < 400$ mb) cloud regions. |
305 |
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Within each of the three regions, clouds are assumed maximally |
306 |
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overlapped, and the cloud cover of the group is the maximum |
307 |
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cloud cover of all the layers in the group. The optical thickness |
308 |
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of a given layer is then scaled for both the direct (as a function of the |
309 |
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solar zenith angle) and diffuse beam radiation |
310 |
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so that the grouped layer reflectance is the same as the original reflectance. |
311 |
molod |
1.13 |
The solar flux is computed for each of eight cloud realizations possible within this |
312 |
molod |
1.1 |
low/middle/high classification, and appropriately averaged to produce the net solar flux. |
313 |
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|
314 |
molod |
1.5 |
\paragraph{Longwave Radiation} |
315 |
molod |
1.1 |
|
316 |
molod |
1.10 |
The longwave radiation package used in the fizhi package is thoroughly described by \cite{chsz:94}. |
317 |
molod |
1.1 |
As described in that document, IR fluxes are computed due to absorption by water vapor, carbon |
318 |
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dioxide, and ozone. The spectral bands together with their absorbers and parameterization methods, |
319 |
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configured for the fizhi package, are shown in Table \ref{tab:fizhi:longwave}. |
320 |
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|
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|
322 |
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\begin{table}[htb] |
323 |
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\begin{center} |
324 |
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{\bf IR Spectral Bands} \\ |
325 |
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\vspace{0.1in} |
326 |
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\begin{tabular}{|c|c|l|c| } |
327 |
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\hline |
328 |
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Band & Spectral Range (cm$^{-1}$) & Absorber & Method \\ \hline |
329 |
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\hline |
330 |
|
|
1 & 0-340 & H$_2$O line & T \\ \hline |
331 |
|
|
2 & 340-540 & H$_2$O line & T \\ \hline |
332 |
|
|
3a & 540-620 & H$_2$O line & K \\ |
333 |
|
|
3b & 620-720 & H$_2$O continuum & S \\ |
334 |
|
|
3b & 720-800 & CO$_2$ & T \\ \hline |
335 |
|
|
4 & 800-980 & H$_2$O line & K \\ |
336 |
|
|
& & H$_2$O continuum & S \\ \hline |
337 |
|
|
& & H$_2$O line & K \\ |
338 |
|
|
5 & 980-1100 & H$_2$O continuum & S \\ |
339 |
|
|
& & O$_3$ & T \\ \hline |
340 |
|
|
6 & 1100-1380 & H$_2$O line & K \\ |
341 |
|
|
& & H$_2$O continuum & S \\ \hline |
342 |
|
|
7 & 1380-1900 & H$_2$O line & T \\ \hline |
343 |
|
|
8 & 1900-3000 & H$_2$O line & K \\ \hline |
344 |
|
|
\hline |
345 |
|
|
\multicolumn{4}{|l|}{ \quad K: {\em k}-distribution method with linear pressure scaling } \\ |
346 |
|
|
\multicolumn{4}{|l|}{ \quad T: Table look-up with temperature and pressure scaling } \\ |
347 |
|
|
\multicolumn{4}{|l|}{ \quad S: One-parameter temperature scaling } \\ |
348 |
|
|
\hline |
349 |
|
|
\end{tabular} |
350 |
|
|
\end{center} |
351 |
|
|
\vspace{0.1in} |
352 |
molod |
1.12 |
\caption{IR Spectral Bands, Absorbers, and Parameterization Method (from \cite{chsz:94})} |
353 |
molod |
1.1 |
\label{tab:fizhi:longwave} |
354 |
|
|
\end{table} |
355 |
|
|
|
356 |
|
|
|
357 |
|
|
The longwave radiation package accurately computes cooling rates for the middle and |
358 |
|
|
lower atmosphere from 0.01 mb to the surface. Errors are $<$ 0.4 C day$^{-1}$ in cooling |
359 |
|
|
rates and $<$ 1\% in fluxes. From Chou and Suarez, it is estimated that the total effect of |
360 |
|
|
neglecting all minor absorption bands and the effects of minor infrared absorbers such as |
361 |
|
|
nitrous oxide (N$_2$O), methane (CH$_4$), and the chlorofluorocarbons (CFCs), is an underestimate |
362 |
|
|
of $\approx$ 5 W/m$^2$ in the downward flux at the surface and an overestimate of $\approx$ 3 W/m$^2$ |
363 |
|
|
in the upward flux at the top of the atmosphere. |
364 |
|
|
|
365 |
|
|
Similar to the procedure used in the shortwave radiation package, clouds are grouped into |
366 |
|
|
three regions catagorized as low/middle/high. |
367 |
|
|
The net clear line-of-site probability $(P)$ between any two levels, $p_1$ and $p_2 \quad (p_2 > p_1)$, |
368 |
|
|
assuming randomly overlapped cloud groups, is simply the product of the probabilities within each group: |
369 |
|
|
|
370 |
|
|
\[ P_{net} = P_{low} \times P_{mid} \times P_{hi} . \] |
371 |
|
|
|
372 |
|
|
Since all clouds within a group are assumed maximally overlapped, the clear line-of-site probability within |
373 |
|
|
a group is given by: |
374 |
|
|
|
375 |
|
|
\[ P_{group} = 1 - F_{max} , \] |
376 |
|
|
|
377 |
|
|
where $F_{max}$ is the maximum cloud fraction encountered between $p_1$ and $p_2$ within that group. |
378 |
|
|
For groups and/or levels outside the range of $p_1$ and $p_2$, a clear line-of-site probability equal to 1 is |
379 |
|
|
assigned. |
380 |
|
|
|
381 |
|
|
|
382 |
molod |
1.5 |
\paragraph{Cloud-Radiation Interaction} |
383 |
molod |
1.1 |
\label{sec:fizhi:radcloud} |
384 |
|
|
|
385 |
|
|
The cloud fractions and diagnosed cloud liquid water produced by moist processes |
386 |
|
|
within the fizhi package are used in the radiation packages to produce cloud-radiative forcing. |
387 |
|
|
The cloud optical thickness associated with large-scale cloudiness is made |
388 |
|
|
proportional to the diagnosed large-scale liquid water, $\ell$, detrained due to super-saturation. |
389 |
|
|
Two values are used corresponding to cloud ice particles and water droplets. |
390 |
|
|
The range of optical thickness for these clouds is given as |
391 |
|
|
|
392 |
|
|
\[ 0.0002 \le \tau_{ice} (mb^{-1}) \le 0.002 \quad\mbox{for}\quad 0 \le \ell \le 2 \quad\mbox{mg/kg} , \] |
393 |
|
|
\[ 0.02 \le \tau_{h_2o} (mb^{-1}) \le 0.2 \quad\mbox{for}\quad 0 \le \ell \le 10 \quad\mbox{mg/kg} . \] |
394 |
|
|
|
395 |
|
|
The partitioning, $\alpha$, between ice particles and water droplets is achieved through a linear scaling |
396 |
|
|
in temperature: |
397 |
|
|
|
398 |
|
|
\[ 0 \le \alpha \le 1 \quad\mbox{for}\quad 233.15 \le T \le 253.15 . \] |
399 |
|
|
|
400 |
|
|
The resulting optical depth associated with large-scale cloudiness is given as |
401 |
|
|
|
402 |
|
|
\[ \tau_{LS} = \alpha \tau_{h_2o} + (1-\alpha)\tau_{ice} . \] |
403 |
|
|
|
404 |
|
|
The optical thickness associated with sub-grid scale convective clouds produced by RAS is given as |
405 |
|
|
|
406 |
|
|
\[ \tau_{RAS} = 0.16 \quad mb^{-1} . \] |
407 |
|
|
|
408 |
|
|
The total optical depth in a given model layer is computed as a weighted average between |
409 |
|
|
the large-scale and sub-grid scale optical depths, normalized by the total cloud fraction in the |
410 |
|
|
layer: |
411 |
|
|
|
412 |
|
|
\[ \tau = \left( {F_{RAS} \,\,\, \tau_{RAS} + F_{LS} \,\,\, \tau_{LS} \over F_{RAS}+F_{LS} } \right) \Delta p, \] |
413 |
|
|
|
414 |
|
|
where $F_{RAS}$ and $F_{LS}$ are the time-averaged cloud fractions associated with RAS and large-scale |
415 |
|
|
processes described in Section \ref{sec:fizhi:clouds}. |
416 |
|
|
The optical thickness for the longwave radiative feedback is assumed to be 75 $\%$ of these values. |
417 |
|
|
|
418 |
|
|
The entire Moist Convective Processes Module is called with a frequency of 10 minutes. |
419 |
|
|
The cloud fraction values are time-averaged over the period between Radiation calls (every 3 |
420 |
|
|
hours). Therefore, in a time-averaged sense, both convective and large-scale |
421 |
|
|
cloudiness can exist in a given grid-box. |
422 |
|
|
|
423 |
molod |
1.12 |
\paragraph{Turbulence}: |
424 |
molod |
1.9 |
|
425 |
molod |
1.1 |
Turbulence is parameterized in the fizhi package to account for its contribution to the |
426 |
|
|
vertical exchange of heat, moisture, and momentum. |
427 |
|
|
The turbulence scheme is invoked every 30 minutes, and employs a backward-implicit iterative |
428 |
|
|
time scheme with an internal time step of 5 minutes. |
429 |
|
|
The tendencies of atmospheric state variables due to turbulent diffusion are calculated using |
430 |
|
|
the diffusion equations: |
431 |
|
|
|
432 |
|
|
\[ |
433 |
|
|
{\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} |
434 |
|
|
= {\pp{}{z} }{(K_m \pp{u}{z})} |
435 |
|
|
\] |
436 |
|
|
\[ |
437 |
|
|
{\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} |
438 |
|
|
= {\pp{}{z} }{(K_m \pp{v}{z})} |
439 |
|
|
\] |
440 |
|
|
\[ |
441 |
|
|
{\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} = |
442 |
|
|
P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} |
443 |
|
|
= P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})} |
444 |
|
|
\] |
445 |
|
|
\[ |
446 |
|
|
{\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} |
447 |
|
|
= {\pp{}{z} }{(K_h \pp{q}{z})} |
448 |
|
|
\] |
449 |
|
|
|
450 |
|
|
Within the atmosphere, the time evolution |
451 |
|
|
of second turbulent moments is explicitly modeled by representing the third moments in terms of |
452 |
|
|
the first and second moments. This approach is known as a second-order closure modeling. |
453 |
|
|
To simplify and streamline the computation of the second moments, the level 2.5 assumption |
454 |
molod |
1.10 |
of Mellor and Yamada (1974) and \cite{yam:77} is employed, in which only the turbulent |
455 |
molod |
1.1 |
kinetic energy (TKE), |
456 |
|
|
|
457 |
|
|
\[ {\h}{q^2}={\overline{{u^{\prime}}^2}}+{\overline{{v^{\prime}}^2}}+{\overline{{w^{\prime}}^2}}, \] |
458 |
|
|
|
459 |
|
|
is solved prognostically and the other second moments are solved diagnostically. |
460 |
|
|
The prognostic equation for TKE allows the scheme to simulate |
461 |
|
|
some of the transient and diffusive effects in the turbulence. The TKE budget equation |
462 |
|
|
is solved numerically using an implicit backward computation of the terms linear in $q^2$ |
463 |
|
|
and is written: |
464 |
|
|
|
465 |
|
|
\[ |
466 |
|
|
{\dd{}{t} ({{\h} q^2})} - { \pp{}{z} ({ {5 \over 3} {{\lambda}_1} q { \pp {}{z} |
467 |
|
|
({\h}q^2)} })} = |
468 |
|
|
{- \overline{{u^{\prime}}{w^{\prime}}} { \pp{U}{z} }} - {\overline{{v^{\prime}}{w^{\prime}}} |
469 |
|
|
{ \pp{V}{z} }} + {{g \over {\Theta_0}}{\overline{{w^{\prime}}{{{\theta}_v}^{\prime}}}} } |
470 |
|
|
- { q^3 \over {{\Lambda} _1} } |
471 |
|
|
\] |
472 |
|
|
|
473 |
|
|
where $q$ is the turbulent velocity, ${u^{\prime}}$, ${v^{\prime}}$, ${w^{\prime}}$ and |
474 |
|
|
${{\theta}^{\prime}}$ are the fluctuating parts of the velocity components and potential |
475 |
|
|
temperature, $U$ and $V$ are the mean velocity components, ${\Theta_0}^{-1}$ is the |
476 |
|
|
coefficient of thermal expansion, and ${{\lambda}_1}$ and ${{\Lambda} _1}$ are constant |
477 |
|
|
multiples of the master length scale, $\ell$, which is designed to be a characteristic measure |
478 |
|
|
of the vertical structure of the turbulent layers. |
479 |
|
|
|
480 |
|
|
The first term on the left-hand side represents the time rate of change of TKE, and |
481 |
|
|
the second term is a representation of the triple correlation, or turbulent |
482 |
|
|
transport term. The first three terms on the right-hand side represent the sources of |
483 |
|
|
TKE due to shear and bouyancy, and the last term on the right hand side is the dissipation |
484 |
|
|
of TKE. |
485 |
|
|
|
486 |
|
|
In the level 2.5 approach, the vertical fluxes of the scalars $\theta_v$ and $q$ and the |
487 |
|
|
wind components $u$ and $v$ are expressed in terms of the diffusion coefficients $K_h$ and |
488 |
molod |
1.10 |
$K_m$, respectively. In the statisically realizable level 2.5 turbulence scheme of |
489 |
|
|
\cite{helflab:88}, these diffusion coefficients are expressed as |
490 |
molod |
1.1 |
|
491 |
|
|
\[ |
492 |
|
|
K_h |
493 |
|
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) \, & \mbox{decaying turbulence} |
494 |
|
|
\\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right. |
495 |
|
|
\] |
496 |
|
|
|
497 |
|
|
and |
498 |
|
|
|
499 |
|
|
\[ |
500 |
|
|
K_m |
501 |
|
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) \, & \mbox{decaying turbulence} |
502 |
|
|
\\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) \, & \mbox{growing turbulence} \end{array} \right. |
503 |
|
|
\] |
504 |
|
|
|
505 |
|
|
where the subscript $e$ refers to the value under conditions of local equillibrium |
506 |
|
|
(obtained from the Level 2.0 Model), $\ell$ is the master length scale related to the |
507 |
|
|
vertical structure of the atmosphere, |
508 |
|
|
and $S_M$ and $S_H$ are functions of $G_H$ and $G_M$, the dimensionless buoyancy and |
509 |
|
|
wind shear parameters, respectively. |
510 |
|
|
Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
511 |
|
|
are functions of the Richardson number: |
512 |
|
|
|
513 |
|
|
\[ |
514 |
|
|
{\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
515 |
|
|
= { {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } . |
516 |
|
|
\] |
517 |
|
|
|
518 |
|
|
Negative values indicate unstable buoyancy and shear, small positive values ($<0.2$) |
519 |
|
|
indicate dominantly unstable shear, and large positive values indicate dominantly stable |
520 |
|
|
stratification. |
521 |
|
|
|
522 |
|
|
Turbulent eddy diffusion coefficients of momentum, heat and moisture in the surface layer, |
523 |
|
|
which corresponds to the lowest GCM level (see \ref{tab:fizhi:sigma}), |
524 |
|
|
are calculated using stability-dependant functions based on Monin-Obukhov theory: |
525 |
|
|
\[ |
526 |
|
|
{K_m} (surface) = C_u \times u_* = C_D W_s |
527 |
|
|
\] |
528 |
|
|
and |
529 |
|
|
\[ |
530 |
|
|
{K_h} (surface) = C_t \times u_* = C_H W_s |
531 |
|
|
\] |
532 |
|
|
where $u_*=C_uW_s$ is the surface friction velocity, |
533 |
|
|
$C_D$ is termed the surface drag coefficient, $C_H$ the heat transfer coefficient, |
534 |
|
|
and $W_s$ is the magnitude of the surface layer wind. |
535 |
|
|
|
536 |
|
|
$C_u$ is the dimensionless exchange coefficient for momentum from the surface layer |
537 |
|
|
similarity functions: |
538 |
|
|
\[ |
539 |
|
|
{C_u} = {u_* \over W_s} = { k \over \psi_{m} } |
540 |
|
|
\] |
541 |
|
|
where k is the Von Karman constant and $\psi_m$ is the surface layer non-dimensional |
542 |
|
|
wind shear given by |
543 |
|
|
\[ |
544 |
|
|
\psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta} . |
545 |
|
|
\] |
546 |
|
|
Here $\zeta$ is the non-dimensional stability parameter, and |
547 |
|
|
$\phi_m$ is the similarity function of $\zeta$ which expresses the stability dependance of |
548 |
|
|
the momentum gradient. The functional form of $\phi_m$ is specified differently for stable and unstable |
549 |
|
|
layers. |
550 |
|
|
|
551 |
|
|
$C_t$ is the dimensionless exchange coefficient for heat and |
552 |
|
|
moisture from the surface layer similarity functions: |
553 |
|
|
\[ |
554 |
|
|
{C_t} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} = |
555 |
|
|
-{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} = |
556 |
|
|
{ k \over { (\psi_{h} + \psi_{g}) } } |
557 |
|
|
\] |
558 |
|
|
where $\psi_h$ is the surface layer non-dimensional temperature gradient given by |
559 |
|
|
\[ |
560 |
|
|
\psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} . |
561 |
|
|
\] |
562 |
|
|
Here $\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of |
563 |
|
|
the temperature and moisture gradients, and is specified differently for stable and unstable |
564 |
molod |
1.10 |
layers according to \cite{helfschu:95}. |
565 |
molod |
1.1 |
|
566 |
|
|
$\psi_g$ is the non-dimensional temperature or moisture gradient in the viscous sublayer, |
567 |
|
|
which is the mosstly laminar region between the surface and the tops of the roughness |
568 |
|
|
elements, in which temperature and moisture gradients can be quite large. |
569 |
molod |
1.10 |
Based on \cite{yagkad:74}: |
570 |
molod |
1.1 |
\[ |
571 |
|
|
\psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} } |
572 |
|
|
(h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2} |
573 |
|
|
\] |
574 |
|
|
where Pr is the Prandtl number for air, $\nu$ is the molecular viscosity, $z_{0}$ is the |
575 |
|
|
surface roughness length, and the subscript {\em ref} refers to a reference value. |
576 |
|
|
$h_{0} = 30z_{0}$ with a maximum value over land of 0.01 |
577 |
|
|
|
578 |
|
|
The surface roughness length over oceans is is a function of the surface-stress velocity, |
579 |
|
|
\[ |
580 |
|
|
{z_0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}} |
581 |
|
|
\] |
582 |
|
|
where the constants are chosen to interpolate between the reciprocal relation of |
583 |
molod |
1.10 |
\cite{kondo:75} for weak winds, and the piecewise linear relation of \cite{larpond:81} |
584 |
molod |
1.1 |
for moderate to large winds. Roughness lengths over land are specified |
585 |
molod |
1.10 |
from the climatology of \cite{dorsell:89}. |
586 |
molod |
1.1 |
|
587 |
|
|
For an unstable surface layer, the stability functions, chosen to interpolate between the |
588 |
|
|
condition of small values of $\beta$ and the convective limit, are the KEYPS function |
589 |
molod |
1.10 |
(\cite{pano:73}) for momentum, and its generalization for heat and moisture: |
590 |
molod |
1.1 |
\[ |
591 |
|
|
{\phi_m}^4 - 18 \zeta {\phi_m}^3 = 1 \hspace{1cm} ; \hspace{1cm} |
592 |
|
|
{\phi_h}^2 - 18 \zeta {\phi_h}^3 = 1 \hspace{1cm} . |
593 |
|
|
\] |
594 |
|
|
The function for heat and moisture assures non-vanishing heat and moisture fluxes as the wind |
595 |
|
|
speed approaches zero. |
596 |
|
|
|
597 |
|
|
For a stable surface layer, the stability functions are the observationally |
598 |
molod |
1.10 |
based functions of \cite{clarke:70}, slightly modified for |
599 |
molod |
1.1 |
the momemtum flux: |
600 |
|
|
\[ |
601 |
|
|
{\phi_m} = { { 1 + 5 {{\zeta}_1} } \over { 1 + 0.00794 {{\zeta}_1} |
602 |
|
|
(1+ 5 {{\zeta}_1}) } } \hspace{1cm} ; \hspace{1cm} |
603 |
|
|
{\phi_h} = { { 1 + 5 {{\zeta}_1} } \over { 1 + 0.00794 {\zeta} |
604 |
|
|
(1+ 5 {{\zeta}_1}) } } . |
605 |
|
|
\] |
606 |
|
|
The moisture flux also depends on a specified evapotranspiration |
607 |
|
|
coefficient, set to unity over oceans and dependant on the climatological ground wetness over |
608 |
|
|
land. |
609 |
|
|
|
610 |
|
|
Once all the diffusion coefficients are calculated, the diffusion equations are solved numerically |
611 |
|
|
using an implicit backward operator. |
612 |
|
|
|
613 |
molod |
1.5 |
\paragraph{Atmospheric Boundary Layer} |
614 |
molod |
1.1 |
|
615 |
|
|
The depth of the atmospheric boundary layer (ABL) is diagnosed by the parameterization as the |
616 |
|
|
level at which the turbulent kinetic energy is reduced to a tenth of its maximum near surface value. |
617 |
|
|
The vertical structure of the ABL is explicitly resolved by the lowest few (3-8) model layers. |
618 |
|
|
|
619 |
molod |
1.5 |
\paragraph{Surface Energy Budget} |
620 |
molod |
1.1 |
|
621 |
|
|
The ground temperature equation is solved as part of the turbulence package |
622 |
|
|
using a backward implicit time differencing scheme: |
623 |
|
|
\[ |
624 |
|
|
C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE |
625 |
|
|
\] |
626 |
|
|
where $R_{sw}$ is the net surface downward shortwave radiative flux and $R_{lw}$ is the |
627 |
|
|
net surface upward longwave radiative flux. |
628 |
|
|
|
629 |
|
|
$H$ is the upward sensible heat flux, given by: |
630 |
|
|
\[ |
631 |
|
|
{H} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{NLAY}) |
632 |
|
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
633 |
|
|
\] |
634 |
|
|
where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific |
635 |
|
|
heat of air at constant pressure, and $\theta$ represents the potential temperature |
636 |
|
|
of the surface and of the lowest $\sigma$-level, respectively. |
637 |
|
|
|
638 |
|
|
The upward latent heat flux, $LE$, is given by |
639 |
|
|
\[ |
640 |
|
|
{LE} = \rho \beta L C_{H} W_s (q_{surface} - q_{NLAY}) |
641 |
|
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
642 |
|
|
\] |
643 |
|
|
where $\beta$ is the fraction of the potential evapotranspiration actually evaporated, |
644 |
|
|
L is the latent heat of evaporation, and $q_{surface}$ and $q_{NLAY}$ are the specific |
645 |
|
|
humidity of the surface and of the lowest $\sigma$-level, respectively. |
646 |
|
|
|
647 |
|
|
The heat conduction through sea ice, $Q_{ice}$, is given by |
648 |
|
|
\[ |
649 |
|
|
{Q_{ice}} = {C_{ti} \over {H_i}} (T_i-T_g) |
650 |
|
|
\] |
651 |
|
|
where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to |
652 |
|
|
be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and $T_g$ is the |
653 |
|
|
surface temperature of the ice. |
654 |
|
|
|
655 |
|
|
$C_g$ is the total heat capacity of the ground, obtained by solving a heat diffusion equation |
656 |
molod |
1.10 |
for the penetration of the diurnal cycle into the ground (\cite{black:77}), and is given by: |
657 |
molod |
1.1 |
\[ |
658 |
|
|
C_g = \sqrt{ {\lambda C_s \over 2\omega} } = \sqrt{(0.386 + 0.536W + 0.15W^2)2\times10^{-3} |
659 |
|
|
{86400 \over 2 \pi} } \, \, . |
660 |
|
|
\] |
661 |
|
|
Here, the thermal conductivity, $\lambda$, is equal to $2\times10^{-3}$ ${ly\over{ sec}} |
662 |
|
|
{cm \over {^oK}}$, |
663 |
|
|
the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided |
664 |
|
|
by $2 \pi$ $radians/ |
665 |
|
|
day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, |
666 |
|
|
is a function of the ground wetness, $W$. |
667 |
|
|
|
668 |
molod |
1.9 |
Land Surface Processes: |
669 |
molod |
1.1 |
|
670 |
molod |
1.5 |
\paragraph{Surface Type} |
671 |
molod |
1.10 |
The fizhi package surface Types are designated using the Koster-Suarez (\cite{ks:91,ks:92}) |
672 |
|
|
Land Surface Model (LSM) mosaic philosophy which allows multiple ``tiles'', or multiple surface |
673 |
|
|
types, in any one grid cell. The Koster-Suarez LSM surface type classifications |
674 |
molod |
1.1 |
are shown in Table \ref{tab:fizhi:surftype}. The surface types and the percent of the grid |
675 |
|
|
cell occupied by any surface type were derived from the surface classification of |
676 |
molod |
1.10 |
\cite{deftow:94}, and information about the location of permanent |
677 |
|
|
ice was obtained from the classifications of \cite{dorsell:89}. |
678 |
molod |
1.13 |
The surface type map for a $1^\circ$ grid is shown in Figure \ref{fig:fizhi:surftype}. |
679 |
molod |
1.1 |
The determination of the land or sea category of surface type was made from NCAR's |
680 |
|
|
10 minute by 10 minute Navy topography |
681 |
|
|
dataset, which includes information about the percentage of water-cover at any point. |
682 |
molod |
1.13 |
The data were averaged to the model's grid resolutions, |
683 |
molod |
1.1 |
and any grid-box whose averaged water percentage was $\geq 60 \%$ was |
684 |
molod |
1.13 |
defined as a water point. The Land-Water designation was further modified |
685 |
molod |
1.1 |
subjectively to ensure sufficient representation from small but isolated land and water regions. |
686 |
|
|
|
687 |
|
|
\begin{table} |
688 |
|
|
\begin{center} |
689 |
|
|
{\bf Surface Type Designation} \\ |
690 |
|
|
\vspace{0.1in} |
691 |
|
|
\begin{tabular}{ |c|l| } |
692 |
|
|
\hline |
693 |
|
|
Type & Vegetation Designation \\ \hline |
694 |
|
|
\hline |
695 |
|
|
1 & Broadleaf Evergreen Trees \\ \hline |
696 |
|
|
2 & Broadleaf Deciduous Trees \\ \hline |
697 |
|
|
3 & Needleleaf Trees \\ \hline |
698 |
|
|
4 & Ground Cover \\ \hline |
699 |
|
|
5 & Broadleaf Shrubs \\ \hline |
700 |
|
|
6 & Dwarf Trees (Tundra) \\ \hline |
701 |
|
|
7 & Bare Soil \\ \hline |
702 |
|
|
8 & Desert (Bright) \\ \hline |
703 |
|
|
9 & Glacier \\ \hline |
704 |
|
|
10 & Desert (Dark) \\ \hline |
705 |
|
|
100 & Ocean \\ \hline |
706 |
|
|
\end{tabular} |
707 |
|
|
\end{center} |
708 |
|
|
\caption{Surface type designations used to compute surface roughness (over land) |
709 |
|
|
and surface albedo.} |
710 |
|
|
\label{tab:fizhi:surftype} |
711 |
|
|
\end{table} |
712 |
|
|
|
713 |
|
|
|
714 |
|
|
\begin{figure*}[htbp] |
715 |
molod |
1.13 |
\begin{center} |
716 |
|
|
\rotatebox{270}{\resizebox{90mm}{!}{\includegraphics{part6/surftypes.eps}}} |
717 |
|
|
\rotatebox{270}{\resizebox{100mm}{!}{\includegraphics{part6/surftypes.descrip.eps}}} |
718 |
|
|
\end{center} |
719 |
|
|
\vspace{0.2in} |
720 |
|
|
\caption {Surface Type Combinations at $1^\circ$ resolution.} |
721 |
molod |
1.1 |
\label{fig:fizhi:surftype} |
722 |
|
|
\end{figure*} |
723 |
|
|
|
724 |
molod |
1.13 |
% \rotatebox{270}{\centerline{ \epsfysize=4in \epsfbox{part6/surftypes.eps}}} |
725 |
|
|
% \rotatebox{270}{\centerline{ \epsfysize=4in \epsfbox{part6/surftypes.descrip.eps}}} |
726 |
|
|
%\begin{figure*}[htbp] |
727 |
|
|
% \centerline{ \epsfysize=4in \epsfbox{part6/surftypes.descrip.ps}} |
728 |
|
|
% \vspace{0.3in} |
729 |
|
|
% \caption {Surface Type Descriptions.} |
730 |
|
|
% \label{fig:fizhi:surftype.desc} |
731 |
|
|
%\end{figure*} |
732 |
molod |
1.1 |
|
733 |
|
|
|
734 |
molod |
1.5 |
\paragraph{Surface Roughness} |
735 |
molod |
1.1 |
The surface roughness length over oceans is computed iteratively with the wind |
736 |
molod |
1.10 |
stress by the surface layer parameterization (\cite{helfschu:95}). |
737 |
|
|
It employs an interpolation between the functions of \cite{larpond:81} |
738 |
|
|
for high winds and of \cite{kondo:75} for weak winds. |
739 |
molod |
1.1 |
|
740 |
|
|
|
741 |
molod |
1.5 |
\paragraph{Albedo} |
742 |
molod |
1.10 |
The surface albedo computation, described in \cite{ks:91}, |
743 |
molod |
1.1 |
employs the ``two stream'' approximation used in Sellers' (1987) Simple Biosphere (SiB) |
744 |
|
|
Model which distinguishes between the direct and diffuse albedos in the visible |
745 |
|
|
and in the near infra-red spectral ranges. The albedos are functions of the observed |
746 |
|
|
leaf area index (a description of the relative orientation of the leaves to the |
747 |
|
|
sun), the greenness fraction, the vegetation type, and the solar zenith angle. |
748 |
|
|
Modifications are made to account for the presence of snow, and its depth relative |
749 |
|
|
to the height of the vegetation elements. |
750 |
|
|
|
751 |
molod |
1.12 |
\paragraph{Gravity Wave Drag}: |
752 |
molod |
1.9 |
|
753 |
molod |
1.12 |
The fizhi package employs the gravity wave drag scheme of \cite{zhouetal:95}). |
754 |
molod |
1.1 |
This scheme is a modified version of Vernekar et al. (1992), |
755 |
|
|
which was based on Alpert et al. (1988) and Helfand et al. (1987). |
756 |
|
|
In this version, the gravity wave stress at the surface is |
757 |
|
|
based on that derived by Pierrehumbert (1986) and is given by: |
758 |
|
|
|
759 |
|
|
\bq |
760 |
|
|
|\vec{\tau}_{sfc}| = {\rho U^3\over{N \ell^*}} \left(F_r^2 \over{1+F_r^2}\right) \, \, , |
761 |
|
|
\eq |
762 |
|
|
|
763 |
|
|
where $F_r = N h /U$ is the Froude number, $N$ is the {\em Brunt - V\"{a}is\"{a}l\"{a}} frequency, $U$ is the |
764 |
|
|
surface wind speed, $h$ is the standard deviation of the sub-grid scale orography, |
765 |
|
|
and $\ell^*$ is the wavelength of the monochromatic gravity wave in the direction of the low-level wind. |
766 |
|
|
A modification introduced by Zhou et al. allows for the momentum flux to |
767 |
|
|
escape through the top of the model, although this effect is small for the current 70-level model. |
768 |
|
|
The subgrid scale standard deviation is defined by $h$, and is not allowed to exceed 400 m. |
769 |
|
|
|
770 |
molod |
1.10 |
The effects of using this scheme within a GCM are shown in \cite{taksz:96}. |
771 |
molod |
1.1 |
Experiments using the gravity wave drag parameterization yielded significant and |
772 |
|
|
beneficial impacts on both the time-mean flow and the transient statistics of the |
773 |
|
|
a GCM climatology, and have eliminated most of the worst dynamically driven biases |
774 |
|
|
in the a GCM simulation. |
775 |
|
|
An examination of the angular momentum budget during climate runs indicates that the |
776 |
|
|
resulting gravity wave torque is similar to the data-driven torque produced by a data |
777 |
|
|
assimilation which was performed without gravity |
778 |
|
|
wave drag. It was shown that the inclusion of gravity wave drag results in |
779 |
|
|
large changes in both the mean flow and in eddy fluxes. |
780 |
|
|
The result is a more |
781 |
|
|
accurate simulation of surface stress (through a reduction in the surface wind strength), |
782 |
|
|
of mountain torque (through a redistribution of mean sea-level pressure), and of momentum |
783 |
|
|
convergence (through a reduction in the flux of westerly momentum by transient flow eddies). |
784 |
|
|
|
785 |
|
|
|
786 |
molod |
1.9 |
Boundary Conditions and other Input Data: |
787 |
molod |
1.1 |
|
788 |
|
|
Required fields which are not explicitly predicted or diagnosed during model execution must |
789 |
|
|
either be prescribed internally or obtained from external data sets. In the fizhi package these |
790 |
|
|
fields include: sea surface temperature, sea ice estent, surface geopotential variance, |
791 |
|
|
vegetation index, and the radiation-related background levels of: ozone, carbon dioxide, |
792 |
|
|
and stratospheric moisture. |
793 |
|
|
|
794 |
molod |
1.13 |
Boundary condition data sets are available at the model's |
795 |
molod |
1.1 |
resolutions for either climatological or yearly varying conditions. |
796 |
|
|
Any frequency of boundary condition data can be used in the fizhi package; |
797 |
|
|
however, the current selection of data is summarized in Table \ref{tab:fizhi:bcdata}\@. |
798 |
|
|
The time mean values are interpolated during each model timestep to the |
799 |
molod |
1.13 |
current time. |
800 |
molod |
1.1 |
|
801 |
|
|
\begin{table}[htb] |
802 |
|
|
\begin{center} |
803 |
|
|
{\bf Fizhi Input Datasets} \\ |
804 |
|
|
\vspace{0.1in} |
805 |
|
|
\begin{tabular}{|l|c|r|} \hline |
806 |
|
|
\multicolumn{1}{|c}{Variable} & \multicolumn{1}{|c}{Frequency} & \multicolumn{1}{|c|}{Years} \\ \hline\hline |
807 |
|
|
Sea Ice Extent & monthly & 1979-current, climatology \\ \hline |
808 |
|
|
Sea Ice Extent & weekly & 1982-current, climatology \\ \hline |
809 |
|
|
Sea Surface Temperature & monthly & 1979-current, climatology \\ \hline |
810 |
|
|
Sea Surface Temperature & weekly & 1982-current, climatology \\ \hline |
811 |
|
|
Zonally Averaged Upper-Level Moisture & monthly & climatology \\ \hline |
812 |
|
|
Zonally Averaged Ozone Concentration & monthly & climatology \\ \hline |
813 |
|
|
\end{tabular} |
814 |
|
|
\end{center} |
815 |
|
|
\caption{Boundary conditions and other input data used in the fizhi package. Also noted are the |
816 |
|
|
current years and frequencies available.} |
817 |
|
|
\label{tab:fizhi:bcdata} |
818 |
|
|
\end{table} |
819 |
|
|
|
820 |
|
|
|
821 |
molod |
1.5 |
\paragraph{Topography and Topography Variance} |
822 |
molod |
1.1 |
|
823 |
|
|
Surface geopotential heights are provided from an averaging of the Navy 10 minute |
824 |
|
|
by 10 minute dataset supplied by the National Center for Atmospheric Research (NCAR) to the |
825 |
|
|
model's grid resolution. The original topography is first rotated to the proper grid-orientation |
826 |
molod |
1.10 |
which is being run, and then averages the data to the model resolution. |
827 |
molod |
1.1 |
|
828 |
molod |
1.10 |
The standard deviation of the subgrid-scale topography is computed by interpolating the 10 minute |
829 |
|
|
data to the model's resolution and re-interpolating back to the 10 minute by 10 minute resolution. |
830 |
molod |
1.1 |
The sub-grid scale variance is constructed based on this smoothed dataset. |
831 |
|
|
|
832 |
|
|
|
833 |
molod |
1.5 |
\paragraph{Upper Level Moisture} |
834 |
molod |
1.1 |
The fizhi package uses climatological water vapor data above 100 mb from the Stratospheric Aerosol and Gas |
835 |
|
|
Experiment (SAGE) as input into the model's radiation packages. The SAGE data is archived |
836 |
|
|
as monthly zonal means at 5$^\circ$ latitudinal resolution. The data is interpolated to the |
837 |
|
|
model's grid location and current time, and blended with the GCM's moisture data. Below 300 mb, |
838 |
|
|
the model's moisture data is used. Above 100 mb, the SAGE data is used. Between 100 and 300 mb, |
839 |
|
|
a linear interpolation (in pressure) is performed using the data from SAGE and the GCM. |
840 |
|
|
|
841 |
molod |
1.8 |
|
842 |
molod |
1.9 |
\subsubsection{Fizhi Diagnostics} |
843 |
molod |
1.8 |
|
844 |
molod |
1.9 |
Fizhi Diagnostic Menu: |
845 |
molod |
1.14 |
\label{sec:pkg:fizhi:diagnostics} |
846 |
molod |
1.8 |
|
847 |
|
|
\begin{tabular}{llll} |
848 |
|
|
\hline\hline |
849 |
|
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
850 |
|
|
\hline |
851 |
|
|
|
852 |
|
|
&\\ |
853 |
|
|
UFLUX & $Newton/m^2$ & 1 |
854 |
|
|
&\begin{minipage}[t]{3in} |
855 |
|
|
{Surface U-Wind Stress on the atmosphere} |
856 |
|
|
\end{minipage}\\ |
857 |
|
|
VFLUX & $Newton/m^2$ & 1 |
858 |
|
|
&\begin{minipage}[t]{3in} |
859 |
|
|
{Surface V-Wind Stress on the atmosphere} |
860 |
|
|
\end{minipage}\\ |
861 |
|
|
HFLUX & $Watts/m^2$ & 1 |
862 |
|
|
&\begin{minipage}[t]{3in} |
863 |
|
|
{Surface Flux of Sensible Heat} |
864 |
|
|
\end{minipage}\\ |
865 |
|
|
EFLUX & $Watts/m^2$ & 1 |
866 |
|
|
&\begin{minipage}[t]{3in} |
867 |
|
|
{Surface Flux of Latent Heat} |
868 |
|
|
\end{minipage}\\ |
869 |
|
|
QICE & $Watts/m^2$ & 1 |
870 |
|
|
&\begin{minipage}[t]{3in} |
871 |
|
|
{Heat Conduction through Sea-Ice} |
872 |
|
|
\end{minipage}\\ |
873 |
|
|
RADLWG & $Watts/m^2$ & 1 |
874 |
|
|
&\begin{minipage}[t]{3in} |
875 |
|
|
{Net upward LW flux at the ground} |
876 |
|
|
\end{minipage}\\ |
877 |
|
|
RADSWG & $Watts/m^2$ & 1 |
878 |
|
|
&\begin{minipage}[t]{3in} |
879 |
|
|
{Net downward SW flux at the ground} |
880 |
|
|
\end{minipage}\\ |
881 |
|
|
RI & $dimensionless$ & Nrphys |
882 |
|
|
&\begin{minipage}[t]{3in} |
883 |
|
|
{Richardson Number} |
884 |
|
|
\end{minipage}\\ |
885 |
|
|
CT & $dimensionless$ & 1 |
886 |
|
|
&\begin{minipage}[t]{3in} |
887 |
|
|
{Surface Drag coefficient for T and Q} |
888 |
|
|
\end{minipage}\\ |
889 |
|
|
CU & $dimensionless$ & 1 |
890 |
|
|
&\begin{minipage}[t]{3in} |
891 |
|
|
{Surface Drag coefficient for U and V} |
892 |
|
|
\end{minipage}\\ |
893 |
|
|
ET & $m^2/sec$ & Nrphys |
894 |
|
|
&\begin{minipage}[t]{3in} |
895 |
|
|
{Diffusivity coefficient for T and Q} |
896 |
|
|
\end{minipage}\\ |
897 |
|
|
EU & $m^2/sec$ & Nrphys |
898 |
|
|
&\begin{minipage}[t]{3in} |
899 |
|
|
{Diffusivity coefficient for U and V} |
900 |
|
|
\end{minipage}\\ |
901 |
|
|
TURBU & $m/sec/day$ & Nrphys |
902 |
|
|
&\begin{minipage}[t]{3in} |
903 |
|
|
{U-Momentum Changes due to Turbulence} |
904 |
|
|
\end{minipage}\\ |
905 |
|
|
TURBV & $m/sec/day$ & Nrphys |
906 |
|
|
&\begin{minipage}[t]{3in} |
907 |
|
|
{V-Momentum Changes due to Turbulence} |
908 |
|
|
\end{minipage}\\ |
909 |
|
|
TURBT & $deg/day$ & Nrphys |
910 |
|
|
&\begin{minipage}[t]{3in} |
911 |
|
|
{Temperature Changes due to Turbulence} |
912 |
|
|
\end{minipage}\\ |
913 |
|
|
TURBQ & $g/kg/day$ & Nrphys |
914 |
|
|
&\begin{minipage}[t]{3in} |
915 |
|
|
{Specific Humidity Changes due to Turbulence} |
916 |
|
|
\end{minipage}\\ |
917 |
|
|
MOISTT & $deg/day$ & Nrphys |
918 |
|
|
&\begin{minipage}[t]{3in} |
919 |
|
|
{Temperature Changes due to Moist Processes} |
920 |
|
|
\end{minipage}\\ |
921 |
|
|
MOISTQ & $g/kg/day$ & Nrphys |
922 |
|
|
&\begin{minipage}[t]{3in} |
923 |
|
|
{Specific Humidity Changes due to Moist Processes} |
924 |
|
|
\end{minipage}\\ |
925 |
|
|
RADLW & $deg/day$ & Nrphys |
926 |
|
|
&\begin{minipage}[t]{3in} |
927 |
|
|
{Net Longwave heating rate for each level} |
928 |
|
|
\end{minipage}\\ |
929 |
|
|
RADSW & $deg/day$ & Nrphys |
930 |
|
|
&\begin{minipage}[t]{3in} |
931 |
|
|
{Net Shortwave heating rate for each level} |
932 |
|
|
\end{minipage}\\ |
933 |
|
|
PREACC & $mm/day$ & 1 |
934 |
|
|
&\begin{minipage}[t]{3in} |
935 |
|
|
{Total Precipitation} |
936 |
|
|
\end{minipage}\\ |
937 |
|
|
PRECON & $mm/day$ & 1 |
938 |
|
|
&\begin{minipage}[t]{3in} |
939 |
|
|
{Convective Precipitation} |
940 |
|
|
\end{minipage}\\ |
941 |
|
|
TUFLUX & $Newton/m^2$ & Nrphys |
942 |
|
|
&\begin{minipage}[t]{3in} |
943 |
|
|
{Turbulent Flux of U-Momentum} |
944 |
|
|
\end{minipage}\\ |
945 |
|
|
TVFLUX & $Newton/m^2$ & Nrphys |
946 |
|
|
&\begin{minipage}[t]{3in} |
947 |
|
|
{Turbulent Flux of V-Momentum} |
948 |
|
|
\end{minipage}\\ |
949 |
|
|
TTFLUX & $Watts/m^2$ & Nrphys |
950 |
|
|
&\begin{minipage}[t]{3in} |
951 |
|
|
{Turbulent Flux of Sensible Heat} |
952 |
|
|
\end{minipage}\\ |
953 |
|
|
\end{tabular} |
954 |
|
|
|
955 |
|
|
\newpage |
956 |
|
|
\vspace*{\fill} |
957 |
|
|
\begin{tabular}{llll} |
958 |
|
|
\hline\hline |
959 |
|
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
960 |
|
|
\hline |
961 |
|
|
|
962 |
|
|
&\\ |
963 |
|
|
TQFLUX & $Watts/m^2$ & Nrphys |
964 |
|
|
&\begin{minipage}[t]{3in} |
965 |
|
|
{Turbulent Flux of Latent Heat} |
966 |
|
|
\end{minipage}\\ |
967 |
|
|
CN & $dimensionless$ & 1 |
968 |
|
|
&\begin{minipage}[t]{3in} |
969 |
|
|
{Neutral Drag Coefficient} |
970 |
|
|
\end{minipage}\\ |
971 |
|
|
WINDS & $m/sec$ & 1 |
972 |
|
|
&\begin{minipage}[t]{3in} |
973 |
|
|
{Surface Wind Speed} |
974 |
|
|
\end{minipage}\\ |
975 |
|
|
DTSRF & $deg$ & 1 |
976 |
|
|
&\begin{minipage}[t]{3in} |
977 |
|
|
{Air/Surface virtual temperature difference} |
978 |
|
|
\end{minipage}\\ |
979 |
|
|
TG & $deg$ & 1 |
980 |
|
|
&\begin{minipage}[t]{3in} |
981 |
|
|
{Ground temperature} |
982 |
|
|
\end{minipage}\\ |
983 |
|
|
TS & $deg$ & 1 |
984 |
|
|
&\begin{minipage}[t]{3in} |
985 |
|
|
{Surface air temperature (Adiabatic from lowest model layer)} |
986 |
|
|
\end{minipage}\\ |
987 |
|
|
DTG & $deg$ & 1 |
988 |
|
|
&\begin{minipage}[t]{3in} |
989 |
|
|
{Ground temperature adjustment} |
990 |
|
|
\end{minipage}\\ |
991 |
|
|
|
992 |
|
|
QG & $g/kg$ & 1 |
993 |
|
|
&\begin{minipage}[t]{3in} |
994 |
|
|
{Ground specific humidity} |
995 |
|
|
\end{minipage}\\ |
996 |
|
|
QS & $g/kg$ & 1 |
997 |
|
|
&\begin{minipage}[t]{3in} |
998 |
|
|
{Saturation surface specific humidity} |
999 |
|
|
\end{minipage}\\ |
1000 |
|
|
TGRLW & $deg$ & 1 |
1001 |
|
|
&\begin{minipage}[t]{3in} |
1002 |
|
|
{Instantaneous ground temperature used as input to the |
1003 |
|
|
Longwave radiation subroutine} |
1004 |
|
|
\end{minipage}\\ |
1005 |
|
|
ST4 & $Watts/m^2$ & 1 |
1006 |
|
|
&\begin{minipage}[t]{3in} |
1007 |
|
|
{Upward Longwave flux at the ground ($\sigma T^4$)} |
1008 |
|
|
\end{minipage}\\ |
1009 |
|
|
OLR & $Watts/m^2$ & 1 |
1010 |
|
|
&\begin{minipage}[t]{3in} |
1011 |
|
|
{Net upward Longwave flux at the top of the model} |
1012 |
|
|
\end{minipage}\\ |
1013 |
|
|
OLRCLR & $Watts/m^2$ & 1 |
1014 |
|
|
&\begin{minipage}[t]{3in} |
1015 |
|
|
{Net upward clearsky Longwave flux at the top of the model} |
1016 |
|
|
\end{minipage}\\ |
1017 |
|
|
LWGCLR & $Watts/m^2$ & 1 |
1018 |
|
|
&\begin{minipage}[t]{3in} |
1019 |
|
|
{Net upward clearsky Longwave flux at the ground} |
1020 |
|
|
\end{minipage}\\ |
1021 |
|
|
LWCLR & $deg/day$ & Nrphys |
1022 |
|
|
&\begin{minipage}[t]{3in} |
1023 |
|
|
{Net clearsky Longwave heating rate for each level} |
1024 |
|
|
\end{minipage}\\ |
1025 |
|
|
TLW & $deg$ & Nrphys |
1026 |
|
|
&\begin{minipage}[t]{3in} |
1027 |
|
|
{Instantaneous temperature used as input to the Longwave radiation |
1028 |
|
|
subroutine} |
1029 |
|
|
\end{minipage}\\ |
1030 |
|
|
SHLW & $g/g$ & Nrphys |
1031 |
|
|
&\begin{minipage}[t]{3in} |
1032 |
|
|
{Instantaneous specific humidity used as input to the Longwave radiation |
1033 |
|
|
subroutine} |
1034 |
|
|
\end{minipage}\\ |
1035 |
|
|
OZLW & $g/g$ & Nrphys |
1036 |
|
|
&\begin{minipage}[t]{3in} |
1037 |
|
|
{Instantaneous ozone used as input to the Longwave radiation |
1038 |
|
|
subroutine} |
1039 |
|
|
\end{minipage}\\ |
1040 |
|
|
CLMOLW & $0-1$ & Nrphys |
1041 |
|
|
&\begin{minipage}[t]{3in} |
1042 |
|
|
{Maximum overlap cloud fraction used in the Longwave radiation |
1043 |
|
|
subroutine} |
1044 |
|
|
\end{minipage}\\ |
1045 |
|
|
CLDTOT & $0-1$ & Nrphys |
1046 |
|
|
&\begin{minipage}[t]{3in} |
1047 |
|
|
{Total cloud fraction used in the Longwave and Shortwave radiation |
1048 |
|
|
subroutines} |
1049 |
|
|
\end{minipage}\\ |
1050 |
|
|
LWGDOWN & $Watts/m^2$ & 1 |
1051 |
|
|
&\begin{minipage}[t]{3in} |
1052 |
|
|
{Downwelling Longwave radiation at the ground} |
1053 |
|
|
\end{minipage}\\ |
1054 |
|
|
GWDT & $deg/day$ & Nrphys |
1055 |
|
|
&\begin{minipage}[t]{3in} |
1056 |
|
|
{Temperature tendency due to Gravity Wave Drag} |
1057 |
|
|
\end{minipage}\\ |
1058 |
|
|
RADSWT & $Watts/m^2$ & 1 |
1059 |
|
|
&\begin{minipage}[t]{3in} |
1060 |
|
|
{Incident Shortwave radiation at the top of the atmosphere} |
1061 |
|
|
\end{minipage}\\ |
1062 |
|
|
TAUCLD & $per 100 mb$ & Nrphys |
1063 |
|
|
&\begin{minipage}[t]{3in} |
1064 |
|
|
{Counted Cloud Optical Depth (non-dimensional) per 100 mb} |
1065 |
|
|
\end{minipage}\\ |
1066 |
|
|
TAUCLDC & $Number$ & Nrphys |
1067 |
|
|
&\begin{minipage}[t]{3in} |
1068 |
|
|
{Cloud Optical Depth Counter} |
1069 |
|
|
\end{minipage}\\ |
1070 |
|
|
\end{tabular} |
1071 |
|
|
\vfill |
1072 |
|
|
|
1073 |
|
|
\newpage |
1074 |
|
|
\vspace*{\fill} |
1075 |
|
|
\begin{tabular}{llll} |
1076 |
|
|
\hline\hline |
1077 |
|
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
1078 |
|
|
\hline |
1079 |
|
|
|
1080 |
|
|
&\\ |
1081 |
|
|
CLDLOW & $0-1$ & Nrphys |
1082 |
|
|
&\begin{minipage}[t]{3in} |
1083 |
|
|
{Low-Level ( 1000-700 hPa) Cloud Fraction (0-1)} |
1084 |
|
|
\end{minipage}\\ |
1085 |
|
|
EVAP & $mm/day$ & 1 |
1086 |
|
|
&\begin{minipage}[t]{3in} |
1087 |
|
|
{Surface evaporation} |
1088 |
|
|
\end{minipage}\\ |
1089 |
|
|
DPDT & $hPa/day$ & 1 |
1090 |
|
|
&\begin{minipage}[t]{3in} |
1091 |
|
|
{Surface Pressure tendency} |
1092 |
|
|
\end{minipage}\\ |
1093 |
|
|
UAVE & $m/sec$ & Nrphys |
1094 |
|
|
&\begin{minipage}[t]{3in} |
1095 |
|
|
{Average U-Wind} |
1096 |
|
|
\end{minipage}\\ |
1097 |
|
|
VAVE & $m/sec$ & Nrphys |
1098 |
|
|
&\begin{minipage}[t]{3in} |
1099 |
|
|
{Average V-Wind} |
1100 |
|
|
\end{minipage}\\ |
1101 |
|
|
TAVE & $deg$ & Nrphys |
1102 |
|
|
&\begin{minipage}[t]{3in} |
1103 |
|
|
{Average Temperature} |
1104 |
|
|
\end{minipage}\\ |
1105 |
|
|
QAVE & $g/kg$ & Nrphys |
1106 |
|
|
&\begin{minipage}[t]{3in} |
1107 |
|
|
{Average Specific Humidity} |
1108 |
|
|
\end{minipage}\\ |
1109 |
|
|
OMEGA & $hPa/day$ & Nrphys |
1110 |
|
|
&\begin{minipage}[t]{3in} |
1111 |
|
|
{Vertical Velocity} |
1112 |
|
|
\end{minipage}\\ |
1113 |
|
|
DUDT & $m/sec/day$ & Nrphys |
1114 |
|
|
&\begin{minipage}[t]{3in} |
1115 |
|
|
{Total U-Wind tendency} |
1116 |
|
|
\end{minipage}\\ |
1117 |
|
|
DVDT & $m/sec/day$ & Nrphys |
1118 |
|
|
&\begin{minipage}[t]{3in} |
1119 |
|
|
{Total V-Wind tendency} |
1120 |
|
|
\end{minipage}\\ |
1121 |
|
|
DTDT & $deg/day$ & Nrphys |
1122 |
|
|
&\begin{minipage}[t]{3in} |
1123 |
|
|
{Total Temperature tendency} |
1124 |
|
|
\end{minipage}\\ |
1125 |
|
|
DQDT & $g/kg/day$ & Nrphys |
1126 |
|
|
&\begin{minipage}[t]{3in} |
1127 |
|
|
{Total Specific Humidity tendency} |
1128 |
|
|
\end{minipage}\\ |
1129 |
|
|
VORT & $10^{-4}/sec$ & Nrphys |
1130 |
|
|
&\begin{minipage}[t]{3in} |
1131 |
|
|
{Relative Vorticity} |
1132 |
|
|
\end{minipage}\\ |
1133 |
|
|
DTLS & $deg/day$ & Nrphys |
1134 |
|
|
&\begin{minipage}[t]{3in} |
1135 |
|
|
{Temperature tendency due to Stratiform Cloud Formation} |
1136 |
|
|
\end{minipage}\\ |
1137 |
|
|
DQLS & $g/kg/day$ & Nrphys |
1138 |
|
|
&\begin{minipage}[t]{3in} |
1139 |
|
|
{Specific Humidity tendency due to Stratiform Cloud Formation} |
1140 |
|
|
\end{minipage}\\ |
1141 |
|
|
USTAR & $m/sec$ & 1 |
1142 |
|
|
&\begin{minipage}[t]{3in} |
1143 |
|
|
{Surface USTAR wind} |
1144 |
|
|
\end{minipage}\\ |
1145 |
|
|
Z0 & $m$ & 1 |
1146 |
|
|
&\begin{minipage}[t]{3in} |
1147 |
|
|
{Surface roughness} |
1148 |
|
|
\end{minipage}\\ |
1149 |
|
|
FRQTRB & $0-1$ & Nrphys-1 |
1150 |
|
|
&\begin{minipage}[t]{3in} |
1151 |
|
|
{Frequency of Turbulence} |
1152 |
|
|
\end{minipage}\\ |
1153 |
|
|
PBL & $mb$ & 1 |
1154 |
|
|
&\begin{minipage}[t]{3in} |
1155 |
|
|
{Planetary Boundary Layer depth} |
1156 |
|
|
\end{minipage}\\ |
1157 |
|
|
SWCLR & $deg/day$ & Nrphys |
1158 |
|
|
&\begin{minipage}[t]{3in} |
1159 |
|
|
{Net clearsky Shortwave heating rate for each level} |
1160 |
|
|
\end{minipage}\\ |
1161 |
|
|
OSR & $Watts/m^2$ & 1 |
1162 |
|
|
&\begin{minipage}[t]{3in} |
1163 |
|
|
{Net downward Shortwave flux at the top of the model} |
1164 |
|
|
\end{minipage}\\ |
1165 |
|
|
OSRCLR & $Watts/m^2$ & 1 |
1166 |
|
|
&\begin{minipage}[t]{3in} |
1167 |
|
|
{Net downward clearsky Shortwave flux at the top of the model} |
1168 |
|
|
\end{minipage}\\ |
1169 |
|
|
CLDMAS & $kg / m^2$ & Nrphys |
1170 |
|
|
&\begin{minipage}[t]{3in} |
1171 |
|
|
{Convective cloud mass flux} |
1172 |
|
|
\end{minipage}\\ |
1173 |
|
|
UAVE & $m/sec$ & Nrphys |
1174 |
|
|
&\begin{minipage}[t]{3in} |
1175 |
|
|
{Time-averaged $u-Wind$} |
1176 |
|
|
\end{minipage}\\ |
1177 |
|
|
\end{tabular} |
1178 |
|
|
\vfill |
1179 |
|
|
|
1180 |
|
|
\newpage |
1181 |
|
|
\vspace*{\fill} |
1182 |
|
|
\begin{tabular}{llll} |
1183 |
|
|
\hline\hline |
1184 |
|
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
1185 |
|
|
\hline |
1186 |
|
|
|
1187 |
|
|
&\\ |
1188 |
|
|
VAVE & $m/sec$ & Nrphys |
1189 |
|
|
&\begin{minipage}[t]{3in} |
1190 |
|
|
{Time-averaged $v-Wind$} |
1191 |
|
|
\end{minipage}\\ |
1192 |
|
|
TAVE & $deg$ & Nrphys |
1193 |
|
|
&\begin{minipage}[t]{3in} |
1194 |
|
|
{Time-averaged $Temperature$} |
1195 |
|
|
\end{minipage}\\ |
1196 |
|
|
QAVE & $g/g$ & Nrphys |
1197 |
|
|
&\begin{minipage}[t]{3in} |
1198 |
|
|
{Time-averaged $Specific \, \, Humidity$} |
1199 |
|
|
\end{minipage}\\ |
1200 |
|
|
RFT & $deg/day$ & Nrphys |
1201 |
|
|
&\begin{minipage}[t]{3in} |
1202 |
|
|
{Temperature tendency due Rayleigh Friction} |
1203 |
|
|
\end{minipage}\\ |
1204 |
|
|
PS & $mb$ & 1 |
1205 |
|
|
&\begin{minipage}[t]{3in} |
1206 |
|
|
{Surface Pressure} |
1207 |
|
|
\end{minipage}\\ |
1208 |
|
|
QQAVE & $(m/sec)^2$ & Nrphys |
1209 |
|
|
&\begin{minipage}[t]{3in} |
1210 |
|
|
{Time-averaged $Turbulent Kinetic Energy$} |
1211 |
|
|
\end{minipage}\\ |
1212 |
|
|
SWGCLR & $Watts/m^2$ & 1 |
1213 |
|
|
&\begin{minipage}[t]{3in} |
1214 |
|
|
{Net downward clearsky Shortwave flux at the ground} |
1215 |
|
|
\end{minipage}\\ |
1216 |
|
|
PAVE & $mb$ & 1 |
1217 |
|
|
&\begin{minipage}[t]{3in} |
1218 |
|
|
{Time-averaged Surface Pressure} |
1219 |
|
|
\end{minipage}\\ |
1220 |
|
|
DIABU & $m/sec/day$ & Nrphys |
1221 |
|
|
&\begin{minipage}[t]{3in} |
1222 |
|
|
{Total Diabatic forcing on $u-Wind$} |
1223 |
|
|
\end{minipage}\\ |
1224 |
|
|
DIABV & $m/sec/day$ & Nrphys |
1225 |
|
|
&\begin{minipage}[t]{3in} |
1226 |
|
|
{Total Diabatic forcing on $v-Wind$} |
1227 |
|
|
\end{minipage}\\ |
1228 |
|
|
DIABT & $deg/day$ & Nrphys |
1229 |
|
|
&\begin{minipage}[t]{3in} |
1230 |
|
|
{Total Diabatic forcing on $Temperature$} |
1231 |
|
|
\end{minipage}\\ |
1232 |
|
|
DIABQ & $g/kg/day$ & Nrphys |
1233 |
|
|
&\begin{minipage}[t]{3in} |
1234 |
|
|
{Total Diabatic forcing on $Specific \, \, Humidity$} |
1235 |
|
|
\end{minipage}\\ |
1236 |
|
|
RFU & $m/sec/day$ & Nrphys |
1237 |
|
|
&\begin{minipage}[t]{3in} |
1238 |
|
|
{U-Wind tendency due to Rayleigh Friction} |
1239 |
|
|
\end{minipage}\\ |
1240 |
|
|
RFV & $m/sec/day$ & Nrphys |
1241 |
|
|
&\begin{minipage}[t]{3in} |
1242 |
|
|
{V-Wind tendency due to Rayleigh Friction} |
1243 |
|
|
\end{minipage}\\ |
1244 |
|
|
GWDU & $m/sec/day$ & Nrphys |
1245 |
|
|
&\begin{minipage}[t]{3in} |
1246 |
|
|
{U-Wind tendency due to Gravity Wave Drag} |
1247 |
|
|
\end{minipage}\\ |
1248 |
|
|
GWDU & $m/sec/day$ & Nrphys |
1249 |
|
|
&\begin{minipage}[t]{3in} |
1250 |
|
|
{V-Wind tendency due to Gravity Wave Drag} |
1251 |
|
|
\end{minipage}\\ |
1252 |
|
|
GWDUS & $N/m^2$ & 1 |
1253 |
|
|
&\begin{minipage}[t]{3in} |
1254 |
|
|
{U-Wind Gravity Wave Drag Stress at Surface} |
1255 |
|
|
\end{minipage}\\ |
1256 |
|
|
GWDVS & $N/m^2$ & 1 |
1257 |
|
|
&\begin{minipage}[t]{3in} |
1258 |
|
|
{V-Wind Gravity Wave Drag Stress at Surface} |
1259 |
|
|
\end{minipage}\\ |
1260 |
|
|
GWDUT & $N/m^2$ & 1 |
1261 |
|
|
&\begin{minipage}[t]{3in} |
1262 |
|
|
{U-Wind Gravity Wave Drag Stress at Top} |
1263 |
|
|
\end{minipage}\\ |
1264 |
|
|
GWDVT & $N/m^2$ & 1 |
1265 |
|
|
&\begin{minipage}[t]{3in} |
1266 |
|
|
{V-Wind Gravity Wave Drag Stress at Top} |
1267 |
|
|
\end{minipage}\\ |
1268 |
|
|
LZRAD & $mg/kg$ & Nrphys |
1269 |
|
|
&\begin{minipage}[t]{3in} |
1270 |
|
|
{Estimated Cloud Liquid Water used in Radiation} |
1271 |
|
|
\end{minipage}\\ |
1272 |
|
|
\end{tabular} |
1273 |
|
|
\vfill |
1274 |
|
|
|
1275 |
|
|
\newpage |
1276 |
|
|
\vspace*{\fill} |
1277 |
|
|
\begin{tabular}{llll} |
1278 |
|
|
\hline\hline |
1279 |
|
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
1280 |
|
|
\hline |
1281 |
|
|
|
1282 |
|
|
&\\ |
1283 |
|
|
SLP & $mb$ & 1 |
1284 |
|
|
&\begin{minipage}[t]{3in} |
1285 |
|
|
{Time-averaged Sea-level Pressure} |
1286 |
|
|
\end{minipage}\\ |
1287 |
|
|
CLDFRC & $0-1$ & 1 |
1288 |
|
|
&\begin{minipage}[t]{3in} |
1289 |
|
|
{Total Cloud Fraction} |
1290 |
|
|
\end{minipage}\\ |
1291 |
|
|
TPW & $gm/cm^2$ & 1 |
1292 |
|
|
&\begin{minipage}[t]{3in} |
1293 |
|
|
{Precipitable water} |
1294 |
|
|
\end{minipage}\\ |
1295 |
|
|
U2M & $m/sec$ & 1 |
1296 |
|
|
&\begin{minipage}[t]{3in} |
1297 |
|
|
{U-Wind at 2 meters} |
1298 |
|
|
\end{minipage}\\ |
1299 |
|
|
V2M & $m/sec$ & 1 |
1300 |
|
|
&\begin{minipage}[t]{3in} |
1301 |
|
|
{V-Wind at 2 meters} |
1302 |
|
|
\end{minipage}\\ |
1303 |
|
|
T2M & $deg$ & 1 |
1304 |
|
|
&\begin{minipage}[t]{3in} |
1305 |
|
|
{Temperature at 2 meters} |
1306 |
|
|
\end{minipage}\\ |
1307 |
|
|
Q2M & $g/kg$ & 1 |
1308 |
|
|
&\begin{minipage}[t]{3in} |
1309 |
|
|
{Specific Humidity at 2 meters} |
1310 |
|
|
\end{minipage}\\ |
1311 |
|
|
U10M & $m/sec$ & 1 |
1312 |
|
|
&\begin{minipage}[t]{3in} |
1313 |
|
|
{U-Wind at 10 meters} |
1314 |
|
|
\end{minipage}\\ |
1315 |
|
|
V10M & $m/sec$ & 1 |
1316 |
|
|
&\begin{minipage}[t]{3in} |
1317 |
|
|
{V-Wind at 10 meters} |
1318 |
|
|
\end{minipage}\\ |
1319 |
|
|
T10M & $deg$ & 1 |
1320 |
|
|
&\begin{minipage}[t]{3in} |
1321 |
|
|
{Temperature at 10 meters} |
1322 |
|
|
\end{minipage}\\ |
1323 |
|
|
Q10M & $g/kg$ & 1 |
1324 |
|
|
&\begin{minipage}[t]{3in} |
1325 |
|
|
{Specific Humidity at 10 meters} |
1326 |
|
|
\end{minipage}\\ |
1327 |
|
|
DTRAIN & $kg/m^2$ & Nrphys |
1328 |
|
|
&\begin{minipage}[t]{3in} |
1329 |
|
|
{Detrainment Cloud Mass Flux} |
1330 |
|
|
\end{minipage}\\ |
1331 |
|
|
QFILL & $g/kg/day$ & Nrphys |
1332 |
|
|
&\begin{minipage}[t]{3in} |
1333 |
|
|
{Filling of negative specific humidity} |
1334 |
|
|
\end{minipage}\\ |
1335 |
|
|
\end{tabular} |
1336 |
|
|
\vspace{1.5in} |
1337 |
|
|
\vfill |
1338 |
|
|
|
1339 |
|
|
\newpage |
1340 |
|
|
\vspace*{\fill} |
1341 |
|
|
\begin{tabular}{llll} |
1342 |
|
|
\hline\hline |
1343 |
|
|
NAME & UNITS & LEVELS & DESCRIPTION \\ |
1344 |
|
|
\hline |
1345 |
|
|
|
1346 |
|
|
&\\ |
1347 |
|
|
DTCONV & $deg/sec$ & Nr |
1348 |
|
|
&\begin{minipage}[t]{3in} |
1349 |
|
|
{Temp Change due to Convection} |
1350 |
|
|
\end{minipage}\\ |
1351 |
|
|
DQCONV & $g/kg/sec$ & Nr |
1352 |
|
|
&\begin{minipage}[t]{3in} |
1353 |
|
|
{Specific Humidity Change due to Convection} |
1354 |
|
|
\end{minipage}\\ |
1355 |
|
|
RELHUM & $percent$ & Nr |
1356 |
|
|
&\begin{minipage}[t]{3in} |
1357 |
|
|
{Relative Humidity} |
1358 |
|
|
\end{minipage}\\ |
1359 |
|
|
PRECLS & $g/m^2/sec$ & 1 |
1360 |
|
|
&\begin{minipage}[t]{3in} |
1361 |
|
|
{Large Scale Precipitation} |
1362 |
|
|
\end{minipage}\\ |
1363 |
|
|
ENPREC & $J/g$ & 1 |
1364 |
|
|
&\begin{minipage}[t]{3in} |
1365 |
|
|
{Energy of Precipitation (snow, rain Temp)} |
1366 |
|
|
\end{minipage}\\ |
1367 |
|
|
\end{tabular} |
1368 |
|
|
\vspace{1.5in} |
1369 |
|
|
\vfill |
1370 |
|
|
|
1371 |
|
|
\newpage |
1372 |
|
|
|
1373 |
molod |
1.9 |
Fizhi Diagnostic Description: |
1374 |
molod |
1.8 |
|
1375 |
|
|
In this section we list and describe the diagnostic quantities available within the |
1376 |
|
|
GCM. The diagnostics are listed in the order that they appear in the |
1377 |
molod |
1.14 |
Diagnostic Menu, Section \ref{sec:pkg:fizhi:diagnostics}. |
1378 |
molod |
1.8 |
In all cases, each diagnostic as currently archived on the output datasets |
1379 |
|
|
is time-averaged over its diagnostic output frequency: |
1380 |
|
|
|
1381 |
|
|
\[ |
1382 |
|
|
{\bf DIAGNOSTIC} = {1 \over TTOT} \sum_{t=1}^{t=TTOT} diag(t) |
1383 |
|
|
\] |
1384 |
|
|
where $TTOT = {{\bf NQDIAG} \over \Delta t}$, {\bf NQDIAG} is the |
1385 |
|
|
output frequency of the diagnostic, and $\Delta t$ is |
1386 |
|
|
the timestep over which the diagnostic is updated. |
1387 |
|
|
|
1388 |
|
|
{ \underline {UFLUX} Surface Zonal Wind Stress on the Atmosphere ($Newton/m^2$) } |
1389 |
|
|
|
1390 |
|
|
The zonal wind stress is the turbulent flux of zonal momentum from |
1391 |
|
|
the surface. |
1392 |
|
|
\[ |
1393 |
|
|
{\bf UFLUX} = - \rho C_D W_s u \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u |
1394 |
|
|
\] |
1395 |
|
|
where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface |
1396 |
|
|
drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum |
1397 |
|
|
(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $u$ is |
1398 |
|
|
the zonal wind in the lowest model layer. |
1399 |
|
|
\\ |
1400 |
|
|
|
1401 |
|
|
|
1402 |
|
|
{ \underline {VFLUX} Surface Meridional Wind Stress on the Atmosphere ($Newton/m^2$) } |
1403 |
|
|
|
1404 |
|
|
The meridional wind stress is the turbulent flux of meridional momentum from |
1405 |
|
|
the surface. |
1406 |
|
|
\[ |
1407 |
|
|
{\bf VFLUX} = - \rho C_D W_s v \hspace{1cm}where: \hspace{.2cm}C_D = C^2_u |
1408 |
|
|
\] |
1409 |
|
|
where $\rho$ = the atmospheric density at the surface, $C_{D}$ is the surface |
1410 |
|
|
drag coefficient, $C_u$ is the dimensionless surface exchange coefficient for momentum |
1411 |
|
|
(see diagnostic number 10), $W_s$ is the magnitude of the surface layer wind, and $v$ is |
1412 |
|
|
the meridional wind in the lowest model layer. |
1413 |
|
|
\\ |
1414 |
|
|
|
1415 |
|
|
{ \underline {HFLUX} Surface Flux of Sensible Heat ($Watts/m^2$) } |
1416 |
|
|
|
1417 |
|
|
The turbulent flux of sensible heat from the surface to the atmosphere is a function of the |
1418 |
|
|
gradient of virtual potential temperature and the eddy exchange coefficient: |
1419 |
|
|
\[ |
1420 |
|
|
{\bf HFLUX} = P^{\kappa}\rho c_{p} C_{H} W_s (\theta_{surface} - \theta_{Nrphys}) |
1421 |
|
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
1422 |
|
|
\] |
1423 |
|
|
where $\rho$ = the atmospheric density at the surface, $c_{p}$ is the specific |
1424 |
|
|
heat of air, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the |
1425 |
|
|
magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient |
1426 |
|
|
for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient |
1427 |
|
|
for heat and moisture (see diagnostic number 9), and $\theta$ is the potential temperature |
1428 |
|
|
at the surface and at the bottom model level. |
1429 |
|
|
\\ |
1430 |
|
|
|
1431 |
|
|
|
1432 |
|
|
{ \underline {EFLUX} Surface Flux of Latent Heat ($Watts/m^2$) } |
1433 |
|
|
|
1434 |
|
|
The turbulent flux of latent heat from the surface to the atmosphere is a function of the |
1435 |
|
|
gradient of moisture, the potential evapotranspiration fraction and the eddy exchange coefficient: |
1436 |
|
|
\[ |
1437 |
|
|
{\bf EFLUX} = \rho \beta L C_{H} W_s (q_{surface} - q_{Nrphys}) |
1438 |
|
|
\hspace{1cm}where: \hspace{.2cm}C_H = C_u C_t |
1439 |
|
|
\] |
1440 |
|
|
where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of |
1441 |
|
|
the potential evapotranspiration actually evaporated, L is the latent |
1442 |
|
|
heat of evaporation, $C_{H}$ is the dimensionless surface heat transfer coefficient, $W_s$ is the |
1443 |
|
|
magnitude of the surface layer wind, $C_u$ is the dimensionless surface exchange coefficient |
1444 |
|
|
for momentum (see diagnostic number 10), $C_t$ is the dimensionless surface exchange coefficient |
1445 |
|
|
for heat and moisture (see diagnostic number 9), and $q_{surface}$ and $q_{Nrphys}$ are the specific |
1446 |
|
|
humidity at the surface and at the bottom model level, respectively. |
1447 |
|
|
\\ |
1448 |
|
|
|
1449 |
|
|
{ \underline {QICE} Heat Conduction Through Sea Ice ($Watts/m^2$) } |
1450 |
|
|
|
1451 |
|
|
Over sea ice there is an additional source of energy at the surface due to the heat |
1452 |
|
|
conduction from the relatively warm ocean through the sea ice. The heat conduction |
1453 |
|
|
through sea ice represents an additional energy source term for the ground temperature equation. |
1454 |
|
|
|
1455 |
|
|
\[ |
1456 |
|
|
{\bf QICE} = {C_{ti} \over {H_i}} (T_i-T_g) |
1457 |
|
|
\] |
1458 |
|
|
|
1459 |
|
|
where $C_{ti}$ is the thermal conductivity of ice, $H_i$ is the ice thickness, assumed to |
1460 |
|
|
be $3 \hspace{.1cm} m$ where sea ice is present, $T_i$ is 273 degrees Kelvin, and |
1461 |
|
|
$T_g$ is the temperature of the sea ice. |
1462 |
|
|
|
1463 |
|
|
NOTE: QICE is not available through model version 5.3, but is available in subsequent versions. |
1464 |
|
|
\\ |
1465 |
|
|
|
1466 |
|
|
|
1467 |
|
|
{ \underline {RADLWG} Net upward Longwave Flux at the surface ($Watts/m^2$)} |
1468 |
|
|
|
1469 |
|
|
\begin{eqnarray*} |
1470 |
|
|
{\bf RADLWG} & = & F_{LW,Nrphys+1}^{Net} \\ |
1471 |
|
|
& = & F_{LW,Nrphys+1}^\uparrow - F_{LW,Nrphys+1}^\downarrow |
1472 |
|
|
\end{eqnarray*} |
1473 |
|
|
\\ |
1474 |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
1475 |
|
|
$F_{LW}^\uparrow$ is |
1476 |
|
|
the upward Longwave flux and $F_{LW}^\downarrow$ is the downward Longwave flux. |
1477 |
|
|
\\ |
1478 |
|
|
|
1479 |
|
|
{ \underline {RADSWG} Net downard shortwave Flux at the surface ($Watts/m^2$)} |
1480 |
|
|
|
1481 |
|
|
\begin{eqnarray*} |
1482 |
|
|
{\bf RADSWG} & = & F_{SW,Nrphys+1}^{Net} \\ |
1483 |
|
|
& = & F_{SW,Nrphys+1}^\downarrow - F_{SW,Nrphys+1}^\uparrow |
1484 |
|
|
\end{eqnarray*} |
1485 |
|
|
\\ |
1486 |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
1487 |
|
|
$F_{SW}^\downarrow$ is |
1488 |
|
|
the downward Shortwave flux and $F_{SW}^\uparrow$ is the upward Shortwave flux. |
1489 |
|
|
\\ |
1490 |
|
|
|
1491 |
|
|
|
1492 |
|
|
\noindent |
1493 |
|
|
{ \underline {RI} Richardson Number} ($dimensionless$) |
1494 |
|
|
|
1495 |
|
|
\noindent |
1496 |
|
|
The non-dimensional stability indicator is the ratio of the buoyancy to the shear: |
1497 |
|
|
\[ |
1498 |
|
|
{\bf RI} = { { {g \over \theta_v} \pp {\theta_v}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
1499 |
|
|
= { {c_p \pp{\theta_v}{z} \pp{P^ \kappa}{z} } \over { (\pp{u}{z})^2 + (\pp{v}{z})^2 } } |
1500 |
|
|
\] |
1501 |
|
|
\\ |
1502 |
|
|
where we used the hydrostatic equation: |
1503 |
|
|
\[ |
1504 |
|
|
{\pp{\Phi}{P^ \kappa}} = c_p \theta_v |
1505 |
|
|
\] |
1506 |
|
|
Negative values indicate unstable buoyancy {\bf{AND}} shear, small positive values ($<0.4$) |
1507 |
|
|
indicate dominantly unstable shear, and large positive values indicate dominantly stable |
1508 |
|
|
stratification. |
1509 |
|
|
\\ |
1510 |
|
|
|
1511 |
|
|
\noindent |
1512 |
|
|
{ \underline {CT} Surface Exchange Coefficient for Temperature and Moisture ($dimensionless$) } |
1513 |
|
|
|
1514 |
|
|
\noindent |
1515 |
|
|
The surface exchange coefficient is obtained from the similarity functions for the stability |
1516 |
|
|
dependant flux profile relationships: |
1517 |
|
|
\[ |
1518 |
|
|
{\bf CT} = -{( {\overline{w^{\prime}\theta^{\prime}}}) \over {u_* \Delta \theta }} = |
1519 |
|
|
-{( {\overline{w^{\prime}q^{\prime}}}) \over {u_* \Delta q }} = |
1520 |
|
|
{ k \over { (\psi_{h} + \psi_{g}) } } |
1521 |
|
|
\] |
1522 |
|
|
where $\psi_h$ is the surface layer non-dimensional temperature change and $\psi_g$ is the |
1523 |
|
|
viscous sublayer non-dimensional temperature or moisture change: |
1524 |
|
|
\[ |
1525 |
|
|
\psi_{h} = {\int_{\zeta_{0}}^{\zeta} {\phi_{h} \over \zeta} d \zeta} \hspace{1cm} and |
1526 |
|
|
\hspace{1cm} \psi_{g} = { 0.55 (Pr^{2/3} - 0.2) \over \nu^{1/2} } |
1527 |
|
|
(h_{0}u_{*} - h_{0_{ref}}u_{*_{ref}})^{1/2} |
1528 |
|
|
\] |
1529 |
|
|
and: |
1530 |
|
|
$h_{0} = 30z_{0}$ with a maximum value over land of 0.01 |
1531 |
|
|
|
1532 |
|
|
\noindent |
1533 |
|
|
$\phi_h$ is the similarity function of $\zeta$, which expresses the stability dependance of |
1534 |
|
|
the temperature and moisture gradients, specified differently for stable and unstable |
1535 |
molod |
1.10 |
layers according to \cite{helfschu:95}. k is the Von Karman constant, $\zeta$ is the |
1536 |
molod |
1.8 |
non-dimensional stability parameter, Pr is the Prandtl number for air, $\nu$ is the molecular |
1537 |
|
|
viscosity, $z_{0}$ is the surface roughness length, $u_*$ is the surface stress velocity |
1538 |
|
|
(see diagnostic number 67), and the subscript ref refers to a reference value. |
1539 |
|
|
\\ |
1540 |
|
|
|
1541 |
|
|
\noindent |
1542 |
|
|
{ \underline {CU} Surface Exchange Coefficient for Momentum ($dimensionless$) } |
1543 |
|
|
|
1544 |
|
|
\noindent |
1545 |
|
|
The surface exchange coefficient is obtained from the similarity functions for the stability |
1546 |
|
|
dependant flux profile relationships: |
1547 |
|
|
\[ |
1548 |
|
|
{\bf CU} = {u_* \over W_s} = { k \over \psi_{m} } |
1549 |
|
|
\] |
1550 |
|
|
where $\psi_m$ is the surface layer non-dimensional wind shear: |
1551 |
|
|
\[ |
1552 |
|
|
\psi_{m} = {\int_{\zeta_{0}}^{\zeta} {\phi_{m} \over \zeta} d \zeta} |
1553 |
|
|
\] |
1554 |
|
|
\noindent |
1555 |
|
|
$\phi_m$ is the similarity function of $\zeta$, which expresses the stability dependance of |
1556 |
|
|
the temperature and moisture gradients, specified differently for stable and unstable layers |
1557 |
molod |
1.10 |
according to \cite{helfschu:95}. k is the Von Karman constant, $\zeta$ is the |
1558 |
molod |
1.8 |
non-dimensional stability parameter, $u_*$ is the surface stress velocity |
1559 |
|
|
(see diagnostic number 67), and $W_s$ is the magnitude of the surface layer wind. |
1560 |
|
|
\\ |
1561 |
|
|
|
1562 |
|
|
\noindent |
1563 |
|
|
{ \underline {ET} Diffusivity Coefficient for Temperature and Moisture ($m^2/sec$) } |
1564 |
|
|
|
1565 |
|
|
\noindent |
1566 |
|
|
In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat or |
1567 |
|
|
moisture flux for the atmosphere above the surface layer can be expressed as a turbulent |
1568 |
|
|
diffusion coefficient $K_h$ times the negative of the gradient of potential temperature |
1569 |
molod |
1.10 |
or moisture. In the \cite{helflab:88} adaptation of this closure, $K_h$ |
1570 |
molod |
1.8 |
takes the form: |
1571 |
|
|
\[ |
1572 |
|
|
{\bf ET} = K_h = -{( {\overline{w^{\prime}\theta_v^{\prime}}}) \over {\pp{\theta_v}{z}} } |
1573 |
|
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_H(G_M,G_H) & \mbox{decaying turbulence} |
1574 |
|
|
\\ { q^2 \over {q_e} } \, \ell \, S_{H}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. |
1575 |
|
|
\] |
1576 |
|
|
where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} |
1577 |
|
|
energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, |
1578 |
|
|
which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer |
1579 |
|
|
depth, |
1580 |
|
|
$S_H$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and |
1581 |
|
|
wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium |
1582 |
|
|
dimensionless buoyancy and wind shear |
1583 |
|
|
parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
1584 |
|
|
are functions of the Richardson number. |
1585 |
|
|
|
1586 |
|
|
\noindent |
1587 |
|
|
For the detailed equations and derivations of the modified level 2.5 closure scheme, |
1588 |
molod |
1.10 |
see \cite{helflab:88}. |
1589 |
molod |
1.8 |
|
1590 |
|
|
\noindent |
1591 |
|
|
In the surface layer, ${\bf {ET}}$ is the exchange coefficient for heat and moisture, |
1592 |
|
|
in units of $m/sec$, given by: |
1593 |
|
|
\[ |
1594 |
|
|
{\bf ET_{Nrphys}} = C_t * u_* = C_H W_s |
1595 |
|
|
\] |
1596 |
|
|
\noindent |
1597 |
|
|
where $C_t$ is the dimensionless exchange coefficient for heat and moisture from the |
1598 |
|
|
surface layer similarity functions (see diagnostic number 9), $u_*$ is the surface |
1599 |
|
|
friction velocity (see diagnostic number 67), $C_H$ is the heat transfer coefficient, |
1600 |
|
|
and $W_s$ is the magnitude of the surface layer wind. |
1601 |
|
|
\\ |
1602 |
|
|
|
1603 |
|
|
\noindent |
1604 |
|
|
{ \underline {EU} Diffusivity Coefficient for Momentum ($m^2/sec$) } |
1605 |
|
|
|
1606 |
|
|
\noindent |
1607 |
|
|
In the level 2.5 version of the Mellor-Yamada (1974) hierarchy, the turbulent heat |
1608 |
|
|
momentum flux for the atmosphere above the surface layer can be expressed as a turbulent |
1609 |
|
|
diffusion coefficient $K_m$ times the negative of the gradient of the u-wind. |
1610 |
molod |
1.10 |
In the \cite{helflab:88} adaptation of this closure, $K_m$ |
1611 |
molod |
1.8 |
takes the form: |
1612 |
|
|
\[ |
1613 |
|
|
{\bf EU} = K_m = -{( {\overline{u^{\prime}w^{\prime}}}) \over {\pp{U}{z}} } |
1614 |
|
|
= \left\{ \begin{array}{l@{\quad\mbox{for}\quad}l} q \, \ell \, S_M(G_M,G_H) & \mbox{decaying turbulence} |
1615 |
|
|
\\ { q^2 \over {q_e} } \, \ell \, S_{M}(G_{M_e},G_{H_e}) & \mbox{growing turbulence} \end{array} \right. |
1616 |
|
|
\] |
1617 |
|
|
\noindent |
1618 |
|
|
where $q$ is the turbulent velocity, or $\sqrt{2*turbulent \hspace{.2cm} kinetic \hspace{.2cm} |
1619 |
|
|
energy}$, $q_e$ is the turbulence velocity derived from the more simple level 2.0 model, |
1620 |
|
|
which describes equilibrium turbulence, $\ell$ is the master length scale related to the layer |
1621 |
|
|
depth, |
1622 |
|
|
$S_M$ is a function of $G_H$ and $G_M$, the dimensionless buoyancy and |
1623 |
|
|
wind shear parameters, respectively, or a function of $G_{H_e}$ and $G_{M_e}$, the equilibrium |
1624 |
|
|
dimensionless buoyancy and wind shear |
1625 |
|
|
parameters. Both $G_H$ and $G_M$, and their equilibrium values $G_{H_e}$ and $G_{M_e}$, |
1626 |
|
|
are functions of the Richardson number. |
1627 |
|
|
|
1628 |
|
|
\noindent |
1629 |
|
|
For the detailed equations and derivations of the modified level 2.5 closure scheme, |
1630 |
molod |
1.10 |
see \cite{helflab:88}. |
1631 |
molod |
1.8 |
|
1632 |
|
|
\noindent |
1633 |
|
|
In the surface layer, ${\bf {EU}}$ is the exchange coefficient for momentum, |
1634 |
|
|
in units of $m/sec$, given by: |
1635 |
|
|
\[ |
1636 |
|
|
{\bf EU_{Nrphys}} = C_u * u_* = C_D W_s |
1637 |
|
|
\] |
1638 |
|
|
\noindent |
1639 |
|
|
where $C_u$ is the dimensionless exchange coefficient for momentum from the surface layer |
1640 |
|
|
similarity functions (see diagnostic number 10), $u_*$ is the surface friction velocity |
1641 |
|
|
(see diagnostic number 67), $C_D$ is the surface drag coefficient, and $W_s$ is the |
1642 |
|
|
magnitude of the surface layer wind. |
1643 |
|
|
\\ |
1644 |
|
|
|
1645 |
|
|
\noindent |
1646 |
|
|
{ \underline {TURBU} Zonal U-Momentum changes due to Turbulence ($m/sec/day$) } |
1647 |
|
|
|
1648 |
|
|
\noindent |
1649 |
|
|
The tendency of U-Momentum due to turbulence is written: |
1650 |
|
|
\[ |
1651 |
|
|
{\bf TURBU} = {\pp{u}{t}}_{turb} = {\pp{}{z} }{(- \overline{u^{\prime}w^{\prime}})} |
1652 |
|
|
= {\pp{}{z} }{(K_m \pp{u}{z})} |
1653 |
|
|
\] |
1654 |
|
|
|
1655 |
|
|
\noindent |
1656 |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
1657 |
|
|
flux of u-momentum in terms of $K_m$, and the equation has the form of a diffusion |
1658 |
|
|
equation. |
1659 |
|
|
|
1660 |
|
|
\noindent |
1661 |
|
|
{ \underline {TURBV} Meridional V-Momentum changes due to Turbulence ($m/sec/day$) } |
1662 |
|
|
|
1663 |
|
|
\noindent |
1664 |
|
|
The tendency of V-Momentum due to turbulence is written: |
1665 |
|
|
\[ |
1666 |
|
|
{\bf TURBV} = {\pp{v}{t}}_{turb} = {\pp{}{z} }{(- \overline{v^{\prime}w^{\prime}})} |
1667 |
|
|
= {\pp{}{z} }{(K_m \pp{v}{z})} |
1668 |
|
|
\] |
1669 |
|
|
|
1670 |
|
|
\noindent |
1671 |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
1672 |
|
|
flux of v-momentum in terms of $K_m$, and the equation has the form of a diffusion |
1673 |
|
|
equation. |
1674 |
|
|
\\ |
1675 |
|
|
|
1676 |
|
|
\noindent |
1677 |
|
|
{ \underline {TURBT} Temperature changes due to Turbulence ($deg/day$) } |
1678 |
|
|
|
1679 |
|
|
\noindent |
1680 |
|
|
The tendency of temperature due to turbulence is written: |
1681 |
|
|
\[ |
1682 |
|
|
{\bf TURBT} = {\pp{T}{t}} = P^{\kappa}{\pp{\theta}{t}}_{turb} = |
1683 |
|
|
P^{\kappa}{\pp{}{z} }{(- \overline{w^{\prime}\theta^{\prime}})} |
1684 |
|
|
= P^{\kappa}{\pp{}{z} }{(K_h \pp{\theta_v}{z})} |
1685 |
|
|
\] |
1686 |
|
|
|
1687 |
|
|
\noindent |
1688 |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
1689 |
|
|
flux of temperature in terms of $K_h$, and the equation has the form of a diffusion |
1690 |
|
|
equation. |
1691 |
|
|
\\ |
1692 |
|
|
|
1693 |
|
|
\noindent |
1694 |
|
|
{ \underline {TURBQ} Specific Humidity changes due to Turbulence ($g/kg/day$) } |
1695 |
|
|
|
1696 |
|
|
\noindent |
1697 |
|
|
The tendency of specific humidity due to turbulence is written: |
1698 |
|
|
\[ |
1699 |
|
|
{\bf TURBQ} = {\pp{q}{t}}_{turb} = {\pp{}{z} }{(- \overline{w^{\prime}q^{\prime}})} |
1700 |
|
|
= {\pp{}{z} }{(K_h \pp{q}{z})} |
1701 |
|
|
\] |
1702 |
|
|
|
1703 |
|
|
\noindent |
1704 |
|
|
The Helfand and Labraga level 2.5 scheme models the turbulent |
1705 |
|
|
flux of temperature in terms of $K_h$, and the equation has the form of a diffusion |
1706 |
|
|
equation. |
1707 |
|
|
\\ |
1708 |
|
|
|
1709 |
|
|
\noindent |
1710 |
|
|
{ \underline {MOISTT} Temperature Changes Due to Moist Processes ($deg/day$) } |
1711 |
|
|
|
1712 |
|
|
\noindent |
1713 |
|
|
\[ |
1714 |
|
|
{\bf MOISTT} = \left. {\pp{T}{t}}\right|_{c} + \left. {\pp{T}{t}} \right|_{ls} |
1715 |
|
|
\] |
1716 |
|
|
where: |
1717 |
|
|
\[ |
1718 |
|
|
\left.{\pp{T}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over c_p} \Gamma_s \right)_i |
1719 |
|
|
\hspace{.4cm} and |
1720 |
|
|
\hspace{.4cm} \left.{\pp{T}{t}}\right|_{ls} = {L \over c_p } (q^*-q) |
1721 |
|
|
\] |
1722 |
|
|
and |
1723 |
|
|
\[ |
1724 |
|
|
\Gamma_s = g \eta \pp{s}{p} |
1725 |
|
|
\] |
1726 |
|
|
|
1727 |
|
|
\noindent |
1728 |
|
|
The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale |
1729 |
|
|
precipitation processes, or supersaturation rain. |
1730 |
|
|
The summation refers to contributions from each cloud type called by RAS. |
1731 |
|
|
The dry static energy is given |
1732 |
|
|
as $s$, the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is |
1733 |
|
|
given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, |
1734 |
|
|
the description of the convective parameterization. The fractional adjustment, or relaxation |
1735 |
|
|
parameter, for each cloud type is given as $\alpha$, while |
1736 |
|
|
$R$ is the rain re-evaporation adjustment. |
1737 |
|
|
\\ |
1738 |
|
|
|
1739 |
|
|
\noindent |
1740 |
|
|
{ \underline {MOISTQ} Specific Humidity Changes Due to Moist Processes ($g/kg/day$) } |
1741 |
|
|
|
1742 |
|
|
\noindent |
1743 |
|
|
\[ |
1744 |
|
|
{\bf MOISTQ} = \left. {\pp{q}{t}}\right|_{c} + \left. {\pp{q}{t}} \right|_{ls} |
1745 |
|
|
\] |
1746 |
|
|
where: |
1747 |
|
|
\[ |
1748 |
|
|
\left.{\pp{q}{t}}\right|_{c} = R \sum_i \left( \alpha { m_B \over {L}}(\Gamma_h-\Gamma_s) \right)_i |
1749 |
|
|
\hspace{.4cm} and |
1750 |
|
|
\hspace{.4cm} \left.{\pp{q}{t}}\right|_{ls} = (q^*-q) |
1751 |
|
|
\] |
1752 |
|
|
and |
1753 |
|
|
\[ |
1754 |
|
|
\Gamma_s = g \eta \pp{s}{p}\hspace{.4cm} and \hspace{.4cm}\Gamma_h = g \eta \pp{h}{p} |
1755 |
|
|
\] |
1756 |
|
|
\noindent |
1757 |
|
|
The subscript $c$ refers to convective processes, while the subscript $ls$ refers to large scale |
1758 |
|
|
precipitation processes, or supersaturation rain. |
1759 |
|
|
The summation refers to contributions from each cloud type called by RAS. |
1760 |
|
|
The dry static energy is given as $s$, |
1761 |
|
|
the moist static energy is given as $h$, |
1762 |
|
|
the convective cloud base mass flux is given as $m_B$, and the cloud entrainment is |
1763 |
|
|
given as $\eta$, which are explicitly defined in Section \ref{sec:fizhi:mc}, |
1764 |
|
|
the description of the convective parameterization. The fractional adjustment, or relaxation |
1765 |
|
|
parameter, for each cloud type is given as $\alpha$, while |
1766 |
|
|
$R$ is the rain re-evaporation adjustment. |
1767 |
|
|
\\ |
1768 |
|
|
|
1769 |
|
|
\noindent |
1770 |
|
|
{ \underline {RADLW} Heating Rate due to Longwave Radiation ($deg/day$) } |
1771 |
|
|
|
1772 |
|
|
\noindent |
1773 |
|
|
The net longwave heating rate is calculated as the vertical divergence of the |
1774 |
|
|
net terrestrial radiative fluxes. |
1775 |
|
|
Both the clear-sky and cloudy-sky longwave fluxes are computed within the |
1776 |
|
|
longwave routine. |
1777 |
|
|
The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. |
1778 |
|
|
For a given cloud fraction, |
1779 |
|
|
the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ |
1780 |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, |
1781 |
|
|
for the upward and downward radiative fluxes. |
1782 |
|
|
(see Section \ref{sec:fizhi:radcloud}). |
1783 |
|
|
The cloudy-sky flux is then obtained as: |
1784 |
|
|
|
1785 |
|
|
\noindent |
1786 |
|
|
\[ |
1787 |
|
|
F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, |
1788 |
|
|
\] |
1789 |
|
|
|
1790 |
|
|
\noindent |
1791 |
|
|
Finally, the net longwave heating rate is calculated as the vertical divergence of the |
1792 |
|
|
net terrestrial radiative fluxes: |
1793 |
|
|
\[ |
1794 |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F_{LW}^{NET} , |
1795 |
|
|
\] |
1796 |
|
|
or |
1797 |
|
|
\[ |
1798 |
|
|
{\bf RADLW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F_{LW}^{NET} . |
1799 |
|
|
\] |
1800 |
|
|
|
1801 |
|
|
\noindent |
1802 |
|
|
where $g$ is the accelation due to gravity, |
1803 |
|
|
$c_p$ is the heat capacity of air at constant pressure, |
1804 |
|
|
and |
1805 |
|
|
\[ |
1806 |
|
|
F_{LW}^{NET} = F_{LW}^\uparrow - F_{LW}^\downarrow |
1807 |
|
|
\] |
1808 |
|
|
\\ |
1809 |
|
|
|
1810 |
|
|
|
1811 |
|
|
\noindent |
1812 |
|
|
{ \underline {RADSW} Heating Rate due to Shortwave Radiation ($deg/day$) } |
1813 |
|
|
|
1814 |
|
|
\noindent |
1815 |
|
|
The net Shortwave heating rate is calculated as the vertical divergence of the |
1816 |
|
|
net solar radiative fluxes. |
1817 |
|
|
The clear-sky and cloudy-sky shortwave fluxes are calculated separately. |
1818 |
|
|
For the clear-sky case, the shortwave fluxes and heating rates are computed with |
1819 |
|
|
both CLMO (maximum overlap cloud fraction) and |
1820 |
|
|
CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). |
1821 |
|
|
The shortwave routine is then called a second time, for the cloudy-sky case, with the |
1822 |
|
|
true time-averaged cloud fractions CLMO |
1823 |
|
|
and CLRO being used. In all cases, a normalized incident shortwave flux is used as |
1824 |
|
|
input at the top of the atmosphere. |
1825 |
|
|
|
1826 |
|
|
\noindent |
1827 |
|
|
The heating rate due to Shortwave Radiation under cloudy skies is defined as: |
1828 |
|
|
\[ |
1829 |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(cloudy)_{SW}^{NET} \cdot {\rm RADSWT}, |
1830 |
|
|
\] |
1831 |
|
|
or |
1832 |
|
|
\[ |
1833 |
|
|
{\bf RADSW} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(cloudy)_{SW}^{NET}\cdot {\rm RADSWT} . |
1834 |
|
|
\] |
1835 |
|
|
|
1836 |
|
|
\noindent |
1837 |
|
|
where $g$ is the accelation due to gravity, |
1838 |
|
|
$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident |
1839 |
|
|
shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and |
1840 |
|
|
\[ |
1841 |
|
|
F(cloudy)_{SW}^{Net} = F(cloudy)_{SW}^\uparrow - F(cloudy)_{SW}^\downarrow |
1842 |
|
|
\] |
1843 |
|
|
\\ |
1844 |
|
|
|
1845 |
|
|
\noindent |
1846 |
|
|
{ \underline {PREACC} Total (Large-scale + Convective) Accumulated Precipition ($mm/day$) } |
1847 |
|
|
|
1848 |
|
|
\noindent |
1849 |
|
|
For a change in specific humidity due to moist processes, $\Delta q_{moist}$, |
1850 |
|
|
the vertical integral or total precipitable amount is given by: |
1851 |
|
|
\[ |
1852 |
|
|
{\bf PREACC} = \int_{surf}^{top} \rho \Delta q_{moist} dz = - \int_{surf}^{top} \Delta q_{moist} |
1853 |
|
|
{dp \over g} = {1 \over g} \int_0^1 \Delta q_{moist} dp |
1854 |
|
|
\] |
1855 |
|
|
\\ |
1856 |
|
|
|
1857 |
|
|
\noindent |
1858 |
|
|
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes |
1859 |
|
|
time step, scaled to $mm/day$. |
1860 |
|
|
\\ |
1861 |
|
|
|
1862 |
|
|
\noindent |
1863 |
|
|
{ \underline {PRECON} Convective Precipition ($mm/day$) } |
1864 |
|
|
|
1865 |
|
|
\noindent |
1866 |
|
|
For a change in specific humidity due to sub-grid scale cumulus convective processes, $\Delta q_{cum}$, |
1867 |
|
|
the vertical integral or total precipitable amount is given by: |
1868 |
|
|
\[ |
1869 |
|
|
{\bf PRECON} = \int_{surf}^{top} \rho \Delta q_{cum} dz = - \int_{surf}^{top} \Delta q_{cum} |
1870 |
|
|
{dp \over g} = {1 \over g} \int_0^1 \Delta q_{cum} dp |
1871 |
|
|
\] |
1872 |
|
|
\\ |
1873 |
|
|
|
1874 |
|
|
\noindent |
1875 |
|
|
A precipitation rate is defined as the vertically integrated moisture adjustment per Moist Processes |
1876 |
|
|
time step, scaled to $mm/day$. |
1877 |
|
|
\\ |
1878 |
|
|
|
1879 |
|
|
\noindent |
1880 |
|
|
{ \underline {TUFLUX} Turbulent Flux of U-Momentum ($Newton/m^2$) } |
1881 |
|
|
|
1882 |
|
|
\noindent |
1883 |
|
|
The turbulent flux of u-momentum is calculated for $diagnostic \hspace{.2cm} purposes |
1884 |
|
|
\hspace{.2cm} only$ from the eddy coefficient for momentum: |
1885 |
|
|
|
1886 |
|
|
\[ |
1887 |
|
|
{\bf TUFLUX} = {\rho } {(\overline{u^{\prime}w^{\prime}})} = |
1888 |
|
|
{\rho } {(- K_m \pp{U}{z})} |
1889 |
|
|
\] |
1890 |
|
|
|
1891 |
|
|
\noindent |
1892 |
|
|
where $\rho$ is the air density, and $K_m$ is the eddy coefficient. |
1893 |
|
|
\\ |
1894 |
|
|
|
1895 |
|
|
\noindent |
1896 |
|
|
{ \underline {TVFLUX} Turbulent Flux of V-Momentum ($Newton/m^2$) } |
1897 |
|
|
|
1898 |
|
|
\noindent |
1899 |
|
|
The turbulent flux of v-momentum is calculated for $diagnostic \hspace{.2cm} purposes |
1900 |
|
|
\hspace{.2cm} only$ from the eddy coefficient for momentum: |
1901 |
|
|
|
1902 |
|
|
\[ |
1903 |
|
|
{\bf TVFLUX} = {\rho } {(\overline{v^{\prime}w^{\prime}})} = |
1904 |
|
|
{\rho } {(- K_m \pp{V}{z})} |
1905 |
|
|
\] |
1906 |
|
|
|
1907 |
|
|
\noindent |
1908 |
|
|
where $\rho$ is the air density, and $K_m$ is the eddy coefficient. |
1909 |
|
|
\\ |
1910 |
|
|
|
1911 |
|
|
|
1912 |
|
|
\noindent |
1913 |
|
|
{ \underline {TTFLUX} Turbulent Flux of Sensible Heat ($Watts/m^2$) } |
1914 |
|
|
|
1915 |
|
|
\noindent |
1916 |
|
|
The turbulent flux of sensible heat is calculated for $diagnostic \hspace{.2cm} purposes |
1917 |
|
|
\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: |
1918 |
|
|
|
1919 |
|
|
\noindent |
1920 |
|
|
\[ |
1921 |
|
|
{\bf TTFLUX} = c_p {\rho } |
1922 |
|
|
P^{\kappa}{(\overline{w^{\prime}\theta^{\prime}})} |
1923 |
|
|
= c_p {\rho } P^{\kappa}{(- K_h \pp{\theta_v}{z})} |
1924 |
|
|
\] |
1925 |
|
|
|
1926 |
|
|
\noindent |
1927 |
|
|
where $\rho$ is the air density, and $K_h$ is the eddy coefficient. |
1928 |
|
|
\\ |
1929 |
|
|
|
1930 |
|
|
|
1931 |
|
|
\noindent |
1932 |
|
|
{ \underline {TQFLUX} Turbulent Flux of Latent Heat ($Watts/m^2$) } |
1933 |
|
|
|
1934 |
|
|
\noindent |
1935 |
|
|
The turbulent flux of latent heat is calculated for $diagnostic \hspace{.2cm} purposes |
1936 |
|
|
\hspace{.2cm} only$ from the eddy coefficient for heat and moisture: |
1937 |
|
|
|
1938 |
|
|
\noindent |
1939 |
|
|
\[ |
1940 |
|
|
{\bf TQFLUX} = {L {\rho } (\overline{w^{\prime}q^{\prime}})} = |
1941 |
|
|
{L {\rho }(- K_h \pp{q}{z})} |
1942 |
|
|
\] |
1943 |
|
|
|
1944 |
|
|
\noindent |
1945 |
|
|
where $\rho$ is the air density, and $K_h$ is the eddy coefficient. |
1946 |
|
|
\\ |
1947 |
|
|
|
1948 |
|
|
|
1949 |
|
|
\noindent |
1950 |
|
|
{ \underline {CN} Neutral Drag Coefficient ($dimensionless$) } |
1951 |
|
|
|
1952 |
|
|
\noindent |
1953 |
|
|
The drag coefficient for momentum obtained by assuming a neutrally stable surface layer: |
1954 |
|
|
\[ |
1955 |
|
|
{\bf CN} = { k \over { \ln({h \over {z_0}})} } |
1956 |
|
|
\] |
1957 |
|
|
|
1958 |
|
|
\noindent |
1959 |
|
|
where $k$ is the Von Karman constant, $h$ is the height of the surface layer, and |
1960 |
|
|
$z_0$ is the surface roughness. |
1961 |
|
|
|
1962 |
|
|
\noindent |
1963 |
|
|
NOTE: CN is not available through model version 5.3, but is available in subsequent |
1964 |
|
|
versions. |
1965 |
|
|
\\ |
1966 |
|
|
|
1967 |
|
|
\noindent |
1968 |
|
|
{ \underline {WINDS} Surface Wind Speed ($meter/sec$) } |
1969 |
|
|
|
1970 |
|
|
\noindent |
1971 |
|
|
The surface wind speed is calculated for the last internal turbulence time step: |
1972 |
|
|
\[ |
1973 |
|
|
{\bf WINDS} = \sqrt{u_{Nrphys}^2 + v_{Nrphys}^2} |
1974 |
|
|
\] |
1975 |
|
|
|
1976 |
|
|
\noindent |
1977 |
|
|
where the subscript $Nrphys$ refers to the lowest model level. |
1978 |
|
|
\\ |
1979 |
|
|
|
1980 |
|
|
\noindent |
1981 |
|
|
{ \underline {DTSRF} Air/Surface Virtual Temperature Difference ($deg \hspace{.1cm} K$) } |
1982 |
|
|
|
1983 |
|
|
\noindent |
1984 |
|
|
The air/surface virtual temperature difference measures the stability of the surface layer: |
1985 |
|
|
\[ |
1986 |
|
|
{\bf DTSRF} = (\theta_{v{Nrphys+1}} - \theta{v_{Nrphys}}) P^{\kappa}_{surf} |
1987 |
|
|
\] |
1988 |
|
|
\noindent |
1989 |
|
|
where |
1990 |
|
|
\[ |
1991 |
|
|
\theta_{v{Nrphys+1}} = { T_g \over {P^{\kappa}_{surf}} } (1 + .609 q_{Nrphys+1}) \hspace{1cm} |
1992 |
|
|
and \hspace{1cm} q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) |
1993 |
|
|
\] |
1994 |
|
|
|
1995 |
|
|
\noindent |
1996 |
|
|
$\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), |
1997 |
|
|
$q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature |
1998 |
|
|
and surface pressure, level $Nrphys$ refers to the lowest model level and level $Nrphys+1$ |
1999 |
|
|
refers to the surface. |
2000 |
|
|
\\ |
2001 |
|
|
|
2002 |
|
|
|
2003 |
|
|
\noindent |
2004 |
|
|
{ \underline {TG} Ground Temperature ($deg \hspace{.1cm} K$) } |
2005 |
|
|
|
2006 |
|
|
\noindent |
2007 |
|
|
The ground temperature equation is solved as part of the turbulence package |
2008 |
|
|
using a backward implicit time differencing scheme: |
2009 |
|
|
\[ |
2010 |
|
|
{\bf TG} \hspace{.1cm} is \hspace{.1cm} obtained \hspace{.1cm} from: \hspace{.1cm} |
2011 |
|
|
C_g\pp{T_g}{t} = R_{sw} - R_{lw} + Q_{ice} - H - LE |
2012 |
|
|
\] |
2013 |
|
|
|
2014 |
|
|
\noindent |
2015 |
|
|
where $R_{sw}$ is the net surface downward shortwave radiative flux, $R_{lw}$ is the |
2016 |
|
|
net surface upward longwave radiative flux, $Q_{ice}$ is the heat conduction through |
2017 |
|
|
sea ice, $H$ is the upward sensible heat flux, $LE$ is the upward latent heat |
2018 |
|
|
flux, and $C_g$ is the total heat capacity of the ground. |
2019 |
|
|
$C_g$ is obtained by solving a heat diffusion equation |
2020 |
molod |
1.10 |
for the penetration of the diurnal cycle into the ground (\cite{black:77}), and is given by: |
2021 |
molod |
1.8 |
\[ |
2022 |
|
|
C_g = \sqrt{ {\lambda C_s \over {2 \omega} } } = \sqrt{(0.386 + 0.536W + 0.15W^2)2x10^{-3} |
2023 |
|
|
{ 86400. \over {2 \pi} } } \, \, . |
2024 |
|
|
\] |
2025 |
|
|
\noindent |
2026 |
|
|
Here, the thermal conductivity, $\lambda$, is equal to $2x10^{-3}$ ${ly\over{ sec}} |
2027 |
|
|
{cm \over {^oK}}$, |
2028 |
|
|
the angular velocity of the earth, $\omega$, is written as $86400$ $sec/day$ divided |
2029 |
|
|
by $2 \pi$ $radians/ |
2030 |
|
|
day$, and the expression for $C_s$, the heat capacity per unit volume at the surface, |
2031 |
|
|
is a function of the ground wetness, $W$. |
2032 |
|
|
\\ |
2033 |
|
|
|
2034 |
|
|
\noindent |
2035 |
|
|
{ \underline {TS} Surface Temperature ($deg \hspace{.1cm} K$) } |
2036 |
|
|
|
2037 |
|
|
\noindent |
2038 |
|
|
The surface temperature estimate is made by assuming that the model's lowest |
2039 |
|
|
layer is well-mixed, and therefore that $\theta$ is constant in that layer. |
2040 |
|
|
The surface temperature is therefore: |
2041 |
|
|
\[ |
2042 |
|
|
{\bf TS} = \theta_{Nrphys} P^{\kappa}_{surf} |
2043 |
|
|
\] |
2044 |
|
|
\\ |
2045 |
|
|
|
2046 |
|
|
\noindent |
2047 |
|
|
{ \underline {DTG} Surface Temperature Adjustment ($deg \hspace{.1cm} K$) } |
2048 |
|
|
|
2049 |
|
|
\noindent |
2050 |
|
|
The change in surface temperature from one turbulence time step to the next, solved |
2051 |
|
|
using the Ground Temperature Equation (see diagnostic number 30) is calculated: |
2052 |
|
|
\[ |
2053 |
|
|
{\bf DTG} = {T_g}^{n} - {T_g}^{n-1} |
2054 |
|
|
\] |
2055 |
|
|
|
2056 |
|
|
\noindent |
2057 |
|
|
where superscript $n$ refers to the new, updated time level, and the superscript $n-1$ |
2058 |
|
|
refers to the value at the previous turbulence time level. |
2059 |
|
|
\\ |
2060 |
|
|
|
2061 |
|
|
\noindent |
2062 |
|
|
{ \underline {QG} Ground Specific Humidity ($g/kg$) } |
2063 |
|
|
|
2064 |
|
|
\noindent |
2065 |
|
|
The ground specific humidity is obtained by interpolating between the specific |
2066 |
|
|
humidity at the lowest model level and the specific humidity of a saturated ground. |
2067 |
|
|
The interpolation is performed using the potential evapotranspiration function: |
2068 |
|
|
\[ |
2069 |
|
|
{\bf QG} = q_{Nrphys+1} = q_{Nrphys} + \beta(q^*(T_g,P_s) - q_{Nrphys}) |
2070 |
|
|
\] |
2071 |
|
|
|
2072 |
|
|
\noindent |
2073 |
|
|
where $\beta$ is the surface potential evapotranspiration coefficient ($\beta=1$ over oceans), |
2074 |
|
|
and $q^*(T_g,P_s)$ is the saturation specific humidity at the ground temperature and surface |
2075 |
|
|
pressure. |
2076 |
|
|
\\ |
2077 |
|
|
|
2078 |
|
|
\noindent |
2079 |
|
|
{ \underline {QS} Saturation Surface Specific Humidity ($g/kg$) } |
2080 |
|
|
|
2081 |
|
|
\noindent |
2082 |
|
|
The surface saturation specific humidity is the saturation specific humidity at |
2083 |
|
|
the ground temprature and surface pressure: |
2084 |
|
|
\[ |
2085 |
|
|
{\bf QS} = q^*(T_g,P_s) |
2086 |
|
|
\] |
2087 |
|
|
\\ |
2088 |
|
|
|
2089 |
|
|
\noindent |
2090 |
|
|
{ \underline {TGRLW} Instantaneous ground temperature used as input to the Longwave |
2091 |
|
|
radiation subroutine (deg)} |
2092 |
|
|
\[ |
2093 |
|
|
{\bf TGRLW} = T_g(\lambda , \phi ,n) |
2094 |
|
|
\] |
2095 |
|
|
\noindent |
2096 |
|
|
where $T_g$ is the model ground temperature at the current time step $n$. |
2097 |
|
|
\\ |
2098 |
|
|
|
2099 |
|
|
|
2100 |
|
|
\noindent |
2101 |
|
|
{ \underline {ST4} Upward Longwave flux at the surface ($Watts/m^2$) } |
2102 |
|
|
\[ |
2103 |
|
|
{\bf ST4} = \sigma T^4 |
2104 |
|
|
\] |
2105 |
|
|
\noindent |
2106 |
|
|
where $\sigma$ is the Stefan-Boltzmann constant and T is the temperature. |
2107 |
|
|
\\ |
2108 |
|
|
|
2109 |
|
|
\noindent |
2110 |
|
|
{ \underline {OLR} Net upward Longwave flux at $p=p_{top}$ ($Watts/m^2$) } |
2111 |
|
|
\[ |
2112 |
|
|
{\bf OLR} = F_{LW,top}^{NET} |
2113 |
|
|
\] |
2114 |
|
|
\noindent |
2115 |
|
|
where top indicates the top of the first model layer. |
2116 |
|
|
In the GCM, $p_{top}$ = 0.0 mb. |
2117 |
|
|
\\ |
2118 |
|
|
|
2119 |
|
|
|
2120 |
|
|
\noindent |
2121 |
|
|
{ \underline {OLRCLR} Net upward clearsky Longwave flux at $p=p_{top}$ ($Watts/m^2$) } |
2122 |
|
|
\[ |
2123 |
|
|
{\bf OLRCLR} = F(clearsky)_{LW,top}^{NET} |
2124 |
|
|
\] |
2125 |
|
|
\noindent |
2126 |
|
|
where top indicates the top of the first model layer. |
2127 |
|
|
In the GCM, $p_{top}$ = 0.0 mb. |
2128 |
|
|
\\ |
2129 |
|
|
|
2130 |
|
|
\noindent |
2131 |
|
|
{ \underline {LWGCLR} Net upward clearsky Longwave flux at the surface ($Watts/m^2$) } |
2132 |
|
|
|
2133 |
|
|
\noindent |
2134 |
|
|
\begin{eqnarray*} |
2135 |
|
|
{\bf LWGCLR} & = & F(clearsky)_{LW,Nrphys+1}^{Net} \\ |
2136 |
|
|
& = & F(clearsky)_{LW,Nrphys+1}^\uparrow - F(clearsky)_{LW,Nrphys+1}^\downarrow |
2137 |
|
|
\end{eqnarray*} |
2138 |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
2139 |
|
|
$F(clearsky)_{LW}^\uparrow$ is |
2140 |
|
|
the upward clearsky Longwave flux and the $F(clearsky)_{LW}^\downarrow$ is the downward clearsky Longwave flux. |
2141 |
|
|
\\ |
2142 |
|
|
|
2143 |
|
|
\noindent |
2144 |
|
|
{ \underline {LWCLR} Heating Rate due to Clearsky Longwave Radiation ($deg/day$) } |
2145 |
|
|
|
2146 |
|
|
\noindent |
2147 |
|
|
The net longwave heating rate is calculated as the vertical divergence of the |
2148 |
|
|
net terrestrial radiative fluxes. |
2149 |
|
|
Both the clear-sky and cloudy-sky longwave fluxes are computed within the |
2150 |
|
|
longwave routine. |
2151 |
|
|
The subroutine calculates the clear-sky flux, $F^{clearsky}_{LW}$, first. |
2152 |
|
|
For a given cloud fraction, |
2153 |
|
|
the clear line-of-sight probability $C(p,p^{\prime})$ is computed from the current level pressure $p$ |
2154 |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, and the model surface pressure, $p^{\prime} = p_{surf}$, |
2155 |
|
|
for the upward and downward radiative fluxes. |
2156 |
|
|
(see Section \ref{sec:fizhi:radcloud}). |
2157 |
|
|
The cloudy-sky flux is then obtained as: |
2158 |
|
|
|
2159 |
|
|
\noindent |
2160 |
|
|
\[ |
2161 |
|
|
F_{LW} = C(p,p') \cdot F^{clearsky}_{LW}, |
2162 |
|
|
\] |
2163 |
|
|
|
2164 |
|
|
\noindent |
2165 |
|
|
Thus, {\bf LWCLR} is defined as the net longwave heating rate due to the |
2166 |
|
|
vertical divergence of the |
2167 |
|
|
clear-sky longwave radiative flux: |
2168 |
|
|
\[ |
2169 |
|
|
\pp{\rho c_p T}{t}_{clearsky} = - {\partial \over \partial z} F(clearsky)_{LW}^{NET} , |
2170 |
|
|
\] |
2171 |
|
|
or |
2172 |
|
|
\[ |
2173 |
|
|
{\bf LWCLR} = \frac{g}{c_p \pi} {\partial \over \partial \sigma} F(clearsky)_{LW}^{NET} . |
2174 |
|
|
\] |
2175 |
|
|
|
2176 |
|
|
\noindent |
2177 |
|
|
where $g$ is the accelation due to gravity, |
2178 |
|
|
$c_p$ is the heat capacity of air at constant pressure, |
2179 |
|
|
and |
2180 |
|
|
\[ |
2181 |
|
|
F(clearsky)_{LW}^{Net} = F(clearsky)_{LW}^\uparrow - F(clearsky)_{LW}^\downarrow |
2182 |
|
|
\] |
2183 |
|
|
\\ |
2184 |
|
|
|
2185 |
|
|
|
2186 |
|
|
\noindent |
2187 |
|
|
{ \underline {TLW} Instantaneous temperature used as input to the Longwave |
2188 |
|
|
radiation subroutine (deg)} |
2189 |
|
|
\[ |
2190 |
|
|
{\bf TLW} = T(\lambda , \phi ,level, n) |
2191 |
|
|
\] |
2192 |
|
|
\noindent |
2193 |
|
|
where $T$ is the model temperature at the current time step $n$. |
2194 |
|
|
\\ |
2195 |
|
|
|
2196 |
|
|
|
2197 |
|
|
\noindent |
2198 |
|
|
{ \underline {SHLW} Instantaneous specific humidity used as input to |
2199 |
|
|
the Longwave radiation subroutine (kg/kg)} |
2200 |
|
|
\[ |
2201 |
|
|
{\bf SHLW} = q(\lambda , \phi , level , n) |
2202 |
|
|
\] |
2203 |
|
|
\noindent |
2204 |
|
|
where $q$ is the model specific humidity at the current time step $n$. |
2205 |
|
|
\\ |
2206 |
|
|
|
2207 |
|
|
|
2208 |
|
|
\noindent |
2209 |
|
|
{ \underline {OZLW} Instantaneous ozone used as input to |
2210 |
|
|
the Longwave radiation subroutine (kg/kg)} |
2211 |
|
|
\[ |
2212 |
|
|
{\bf OZLW} = {\rm OZ}(\lambda , \phi , level , n) |
2213 |
|
|
\] |
2214 |
|
|
\noindent |
2215 |
|
|
where $\rm OZ$ is the interpolated ozone data set from the climatological monthly |
2216 |
|
|
mean zonally averaged ozone data set. |
2217 |
|
|
\\ |
2218 |
|
|
|
2219 |
|
|
|
2220 |
|
|
\noindent |
2221 |
|
|
{ \underline {CLMOLW} Maximum Overlap cloud fraction used in LW Radiation ($0-1$) } |
2222 |
|
|
|
2223 |
|
|
\noindent |
2224 |
|
|
{\bf CLMOLW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed |
2225 |
|
|
Arakawa/Schubert Convection scheme and will be used in the Longwave Radiation algorithm. These are |
2226 |
|
|
convective clouds whose radiative characteristics are assumed to be correlated in the vertical. |
2227 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
2228 |
|
|
\[ |
2229 |
|
|
{\bf CLMOLW} = CLMO_{RAS,LW}(\lambda, \phi, level ) |
2230 |
|
|
\] |
2231 |
|
|
\\ |
2232 |
|
|
|
2233 |
|
|
|
2234 |
|
|
{ \underline {CLDTOT} Total cloud fraction used in LW and SW Radiation ($0-1$) } |
2235 |
|
|
|
2236 |
|
|
{\bf CLDTOT} is the time-averaged total cloud fraction that has been filled by the Relaxed |
2237 |
|
|
Arakawa/Schubert and Large-scale Convection schemes and will be used in the Longwave and Shortwave |
2238 |
|
|
Radiation packages. |
2239 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
2240 |
|
|
\[ |
2241 |
|
|
{\bf CLDTOT} = F_{RAS} + F_{LS} |
2242 |
|
|
\] |
2243 |
|
|
\\ |
2244 |
|
|
where $F_{RAS}$ is the time-averaged cloud fraction due to sub-grid scale convection, and $F_{LS}$ is the |
2245 |
|
|
time-averaged cloud fraction due to precipitating and non-precipitating large-scale moist processes. |
2246 |
|
|
\\ |
2247 |
|
|
|
2248 |
|
|
|
2249 |
|
|
\noindent |
2250 |
|
|
{ \underline {CLMOSW} Maximum Overlap cloud fraction used in SW Radiation ($0-1$) } |
2251 |
|
|
|
2252 |
|
|
\noindent |
2253 |
|
|
{\bf CLMOSW} is the time-averaged maximum overlap cloud fraction that has been filled by the Relaxed |
2254 |
|
|
Arakawa/Schubert Convection scheme and will be used in the Shortwave Radiation algorithm. These are |
2255 |
|
|
convective clouds whose radiative characteristics are assumed to be correlated in the vertical. |
2256 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
2257 |
|
|
\[ |
2258 |
|
|
{\bf CLMOSW} = CLMO_{RAS,SW}(\lambda, \phi, level ) |
2259 |
|
|
\] |
2260 |
|
|
\\ |
2261 |
|
|
|
2262 |
|
|
\noindent |
2263 |
|
|
{ \underline {CLROSW} Random Overlap cloud fraction used in SW Radiation ($0-1$) } |
2264 |
|
|
|
2265 |
|
|
\noindent |
2266 |
|
|
{\bf CLROSW} is the time-averaged random overlap cloud fraction that has been filled by the Relaxed |
2267 |
|
|
Arakawa/Schubert and Large-scale Convection schemes and will be used in the Shortwave |
2268 |
|
|
Radiation algorithm. These are |
2269 |
|
|
convective and large-scale clouds whose radiative characteristics are not |
2270 |
|
|
assumed to be correlated in the vertical. |
2271 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
2272 |
|
|
\[ |
2273 |
|
|
{\bf CLROSW} = CLRO_{RAS,Large Scale,SW}(\lambda, \phi, level ) |
2274 |
|
|
\] |
2275 |
|
|
\\ |
2276 |
|
|
|
2277 |
|
|
\noindent |
2278 |
|
|
{ \underline {RADSWT} Incident Shortwave radiation at the top of the atmosphere ($Watts/m^2$) } |
2279 |
|
|
\[ |
2280 |
|
|
{\bf RADSWT} = {\frac{S_0}{R_a^2}} \cdot cos \phi_z |
2281 |
|
|
\] |
2282 |
|
|
\noindent |
2283 |
|
|
where $S_0$, is the extra-terrestial solar contant, |
2284 |
|
|
$R_a$ is the earth-sun distance in Astronomical Units, |
2285 |
|
|
and $cos \phi_z$ is the cosine of the zenith angle. |
2286 |
|
|
It should be noted that {\bf RADSWT}, as well as |
2287 |
|
|
{\bf OSR} and {\bf OSRCLR}, |
2288 |
|
|
are calculated at the top of the atmosphere (p=0 mb). However, the |
2289 |
|
|
{\bf OLR} and {\bf OLRCLR} diagnostics are currently |
2290 |
|
|
calculated at $p= p_{top}$ (0.0 mb for the GCM). |
2291 |
|
|
\\ |
2292 |
|
|
|
2293 |
|
|
\noindent |
2294 |
|
|
{ \underline {EVAP} Surface Evaporation ($mm/day$) } |
2295 |
|
|
|
2296 |
|
|
\noindent |
2297 |
|
|
The surface evaporation is a function of the gradient of moisture, the potential |
2298 |
|
|
evapotranspiration fraction and the eddy exchange coefficient: |
2299 |
|
|
\[ |
2300 |
|
|
{\bf EVAP} = \rho \beta K_{h} (q_{surface} - q_{Nrphys}) |
2301 |
|
|
\] |
2302 |
|
|
where $\rho$ = the atmospheric density at the surface, $\beta$ is the fraction of |
2303 |
|
|
the potential evapotranspiration actually evaporated ($\beta=1$ over oceans), $K_{h}$ is the |
2304 |
|
|
turbulent eddy exchange coefficient for heat and moisture at the surface in $m/sec$ and |
2305 |
|
|
$q{surface}$ and $q_{Nrphys}$ are the specific humidity at the surface (see diagnostic |
2306 |
|
|
number 34) and at the bottom model level, respectively. |
2307 |
|
|
\\ |
2308 |
|
|
|
2309 |
|
|
\noindent |
2310 |
|
|
{ \underline {DUDT} Total Zonal U-Wind Tendency ($m/sec/day$) } |
2311 |
|
|
|
2312 |
|
|
\noindent |
2313 |
|
|
{\bf DUDT} is the total time-tendency of the Zonal U-Wind due to Hydrodynamic, Diabatic, |
2314 |
|
|
and Analysis forcing. |
2315 |
|
|
\[ |
2316 |
|
|
{\bf DUDT} = \pp{u}{t}_{Dynamics} + \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} |
2317 |
|
|
\] |
2318 |
|
|
\\ |
2319 |
|
|
|
2320 |
|
|
\noindent |
2321 |
|
|
{ \underline {DVDT} Total Zonal V-Wind Tendency ($m/sec/day$) } |
2322 |
|
|
|
2323 |
|
|
\noindent |
2324 |
|
|
{\bf DVDT} is the total time-tendency of the Meridional V-Wind due to Hydrodynamic, Diabatic, |
2325 |
|
|
and Analysis forcing. |
2326 |
|
|
\[ |
2327 |
|
|
{\bf DVDT} = \pp{v}{t}_{Dynamics} + \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} |
2328 |
|
|
\] |
2329 |
|
|
\\ |
2330 |
|
|
|
2331 |
|
|
\noindent |
2332 |
|
|
{ \underline {DTDT} Total Temperature Tendency ($deg/day$) } |
2333 |
|
|
|
2334 |
|
|
\noindent |
2335 |
|
|
{\bf DTDT} is the total time-tendency of Temperature due to Hydrodynamic, Diabatic, |
2336 |
|
|
and Analysis forcing. |
2337 |
|
|
\begin{eqnarray*} |
2338 |
|
|
{\bf DTDT} & = & \pp{T}{t}_{Dynamics} + \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
2339 |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} |
2340 |
|
|
\end{eqnarray*} |
2341 |
|
|
\\ |
2342 |
|
|
|
2343 |
|
|
\noindent |
2344 |
|
|
{ \underline {DQDT} Total Specific Humidity Tendency ($g/kg/day$) } |
2345 |
|
|
|
2346 |
|
|
\noindent |
2347 |
|
|
{\bf DQDT} is the total time-tendency of Specific Humidity due to Hydrodynamic, Diabatic, |
2348 |
|
|
and Analysis forcing. |
2349 |
|
|
\[ |
2350 |
|
|
{\bf DQDT} = \pp{q}{t}_{Dynamics} + \pp{q}{t}_{Moist Processes} |
2351 |
|
|
+ \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} |
2352 |
|
|
\] |
2353 |
|
|
\\ |
2354 |
|
|
|
2355 |
|
|
\noindent |
2356 |
|
|
{ \underline {USTAR} Surface-Stress Velocity ($m/sec$) } |
2357 |
|
|
|
2358 |
|
|
\noindent |
2359 |
|
|
The surface stress velocity, or the friction velocity, is the wind speed at |
2360 |
|
|
the surface layer top impeded by the surface drag: |
2361 |
|
|
\[ |
2362 |
|
|
{\bf USTAR} = C_uW_s \hspace{1cm}where: \hspace{.2cm} |
2363 |
|
|
C_u = {k \over {\psi_m} } |
2364 |
|
|
\] |
2365 |
|
|
|
2366 |
|
|
\noindent |
2367 |
|
|
$C_u$ is the non-dimensional surface drag coefficient (see diagnostic |
2368 |
|
|
number 10), and $W_s$ is the surface wind speed (see diagnostic number 28). |
2369 |
|
|
|
2370 |
|
|
\noindent |
2371 |
|
|
{ \underline {Z0} Surface Roughness Length ($m$) } |
2372 |
|
|
|
2373 |
|
|
\noindent |
2374 |
|
|
Over the land surface, the surface roughness length is interpolated to the local |
2375 |
molod |
1.10 |
time from the monthly mean data of \cite{dorsell:89}. Over the ocean, |
2376 |
molod |
1.8 |
the roughness length is a function of the surface-stress velocity, $u_*$. |
2377 |
|
|
\[ |
2378 |
|
|
{\bf Z0} = c_1u^3_* + c_2u^2_* + c_3u_* + c_4 + {c_5 \over {u_*}} |
2379 |
|
|
\] |
2380 |
|
|
|
2381 |
|
|
\noindent |
2382 |
|
|
where the constants are chosen to interpolate between the reciprocal relation of |
2383 |
molod |
1.10 |
\cite{kondo:75} for weak winds, and the piecewise linear relation of \cite{larpond:81} |
2384 |
molod |
1.8 |
for moderate to large winds. |
2385 |
|
|
\\ |
2386 |
|
|
|
2387 |
|
|
\noindent |
2388 |
|
|
{ \underline {FRQTRB} Frequency of Turbulence ($0-1$) } |
2389 |
|
|
|
2390 |
|
|
\noindent |
2391 |
|
|
The fraction of time when turbulence is present is defined as the fraction of |
2392 |
|
|
time when the turbulent kinetic energy exceeds some minimum value, defined here |
2393 |
|
|
to be $0.005 \hspace{.1cm}m^2/sec^2$. When this criterion is met, a counter is |
2394 |
|
|
incremented. The fraction over the averaging interval is reported. |
2395 |
|
|
\\ |
2396 |
|
|
|
2397 |
|
|
\noindent |
2398 |
|
|
{ \underline {PBL} Planetary Boundary Layer Depth ($mb$) } |
2399 |
|
|
|
2400 |
|
|
\noindent |
2401 |
|
|
The depth of the PBL is defined by the turbulence parameterization to be the |
2402 |
|
|
depth at which the turbulent kinetic energy reduces to ten percent of its surface |
2403 |
|
|
value. |
2404 |
|
|
|
2405 |
|
|
\[ |
2406 |
|
|
{\bf PBL} = P_{PBL} - P_{surface} |
2407 |
|
|
\] |
2408 |
|
|
|
2409 |
|
|
\noindent |
2410 |
|
|
where $P_{PBL}$ is the pressure in $mb$ at which the turbulent kinetic energy |
2411 |
|
|
reaches one tenth of its surface value, and $P_s$ is the surface pressure. |
2412 |
|
|
\\ |
2413 |
|
|
|
2414 |
|
|
\noindent |
2415 |
|
|
{ \underline {SWCLR} Clear sky Heating Rate due to Shortwave Radiation ($deg/day$) } |
2416 |
|
|
|
2417 |
|
|
\noindent |
2418 |
|
|
The net Shortwave heating rate is calculated as the vertical divergence of the |
2419 |
|
|
net solar radiative fluxes. |
2420 |
|
|
The clear-sky and cloudy-sky shortwave fluxes are calculated separately. |
2421 |
|
|
For the clear-sky case, the shortwave fluxes and heating rates are computed with |
2422 |
|
|
both CLMO (maximum overlap cloud fraction) and |
2423 |
|
|
CLRO (random overlap cloud fraction) set to zero (see Section \ref{sec:fizhi:radcloud}). |
2424 |
|
|
The shortwave routine is then called a second time, for the cloudy-sky case, with the |
2425 |
|
|
true time-averaged cloud fractions CLMO |
2426 |
|
|
and CLRO being used. In all cases, a normalized incident shortwave flux is used as |
2427 |
|
|
input at the top of the atmosphere. |
2428 |
|
|
|
2429 |
|
|
\noindent |
2430 |
|
|
The heating rate due to Shortwave Radiation under clear skies is defined as: |
2431 |
|
|
\[ |
2432 |
|
|
\pp{\rho c_p T}{t} = - {\partial \over \partial z} F(clear)_{SW}^{NET} \cdot {\rm RADSWT}, |
2433 |
|
|
\] |
2434 |
|
|
or |
2435 |
|
|
\[ |
2436 |
|
|
{\bf SWCLR} = \frac{g}{c_p } {\partial \over \partial p} F(clear)_{SW}^{NET}\cdot {\rm RADSWT} . |
2437 |
|
|
\] |
2438 |
|
|
|
2439 |
|
|
\noindent |
2440 |
|
|
where $g$ is the accelation due to gravity, |
2441 |
|
|
$c_p$ is the heat capacity of air at constant pressure, RADSWT is the true incident |
2442 |
|
|
shortwave radiation at the top of the atmosphere (See Diagnostic \#48), and |
2443 |
|
|
\[ |
2444 |
|
|
F(clear)_{SW}^{Net} = F(clear)_{SW}^\uparrow - F(clear)_{SW}^\downarrow |
2445 |
|
|
\] |
2446 |
|
|
\\ |
2447 |
|
|
|
2448 |
|
|
\noindent |
2449 |
|
|
{ \underline {OSR} Net upward Shortwave flux at the top of the model ($Watts/m^2$) } |
2450 |
|
|
\[ |
2451 |
|
|
{\bf OSR} = F_{SW,top}^{NET} |
2452 |
|
|
\] |
2453 |
|
|
\noindent |
2454 |
|
|
where top indicates the top of the first model layer used in the shortwave radiation |
2455 |
|
|
routine. |
2456 |
|
|
In the GCM, $p_{SW_{top}}$ = 0 mb. |
2457 |
|
|
\\ |
2458 |
|
|
|
2459 |
|
|
\noindent |
2460 |
|
|
{ \underline {OSRCLR} Net upward clearsky Shortwave flux at the top of the model ($Watts/m^2$) } |
2461 |
|
|
\[ |
2462 |
|
|
{\bf OSRCLR} = F(clearsky)_{SW,top}^{NET} |
2463 |
|
|
\] |
2464 |
|
|
\noindent |
2465 |
|
|
where top indicates the top of the first model layer used in the shortwave radiation |
2466 |
|
|
routine. |
2467 |
|
|
In the GCM, $p_{SW_{top}}$ = 0 mb. |
2468 |
|
|
\\ |
2469 |
|
|
|
2470 |
|
|
|
2471 |
|
|
\noindent |
2472 |
|
|
{ \underline {CLDMAS} Convective Cloud Mass Flux ($kg/m^2$) } |
2473 |
|
|
|
2474 |
|
|
\noindent |
2475 |
|
|
The amount of cloud mass moved per RAS timestep from all convective clouds is written: |
2476 |
|
|
\[ |
2477 |
|
|
{\bf CLDMAS} = \eta m_B |
2478 |
|
|
\] |
2479 |
|
|
where $\eta$ is the entrainment, normalized by the cloud base mass flux, and $m_B$ is |
2480 |
|
|
the cloud base mass flux. $m_B$ and $\eta$ are defined explicitly in Section \ref{sec:fizhi:mc}, the |
2481 |
|
|
description of the convective parameterization. |
2482 |
|
|
\\ |
2483 |
|
|
|
2484 |
|
|
|
2485 |
|
|
|
2486 |
|
|
\noindent |
2487 |
|
|
{ \underline {UAVE} Time-Averaged Zonal U-Wind ($m/sec$) } |
2488 |
|
|
|
2489 |
|
|
\noindent |
2490 |
|
|
The diagnostic {\bf UAVE} is simply the time-averaged Zonal U-Wind over |
2491 |
|
|
the {\bf NUAVE} output frequency. This is contrasted to the instantaneous |
2492 |
|
|
Zonal U-Wind which is archived on the Prognostic Output data stream. |
2493 |
|
|
\[ |
2494 |
|
|
{\bf UAVE} = u(\lambda, \phi, level , t) |
2495 |
|
|
\] |
2496 |
|
|
\\ |
2497 |
|
|
Note, {\bf UAVE} is computed and stored on the staggered C-grid. |
2498 |
|
|
\\ |
2499 |
|
|
|
2500 |
|
|
\noindent |
2501 |
|
|
{ \underline {VAVE} Time-Averaged Meridional V-Wind ($m/sec$) } |
2502 |
|
|
|
2503 |
|
|
\noindent |
2504 |
|
|
The diagnostic {\bf VAVE} is simply the time-averaged Meridional V-Wind over |
2505 |
|
|
the {\bf NVAVE} output frequency. This is contrasted to the instantaneous |
2506 |
|
|
Meridional V-Wind which is archived on the Prognostic Output data stream. |
2507 |
|
|
\[ |
2508 |
|
|
{\bf VAVE} = v(\lambda, \phi, level , t) |
2509 |
|
|
\] |
2510 |
|
|
\\ |
2511 |
|
|
Note, {\bf VAVE} is computed and stored on the staggered C-grid. |
2512 |
|
|
\\ |
2513 |
|
|
|
2514 |
|
|
\noindent |
2515 |
|
|
{ \underline {TAVE} Time-Averaged Temperature ($Kelvin$) } |
2516 |
|
|
|
2517 |
|
|
\noindent |
2518 |
|
|
The diagnostic {\bf TAVE} is simply the time-averaged Temperature over |
2519 |
|
|
the {\bf NTAVE} output frequency. This is contrasted to the instantaneous |
2520 |
|
|
Temperature which is archived on the Prognostic Output data stream. |
2521 |
|
|
\[ |
2522 |
|
|
{\bf TAVE} = T(\lambda, \phi, level , t) |
2523 |
|
|
\] |
2524 |
|
|
\\ |
2525 |
|
|
|
2526 |
|
|
\noindent |
2527 |
|
|
{ \underline {QAVE} Time-Averaged Specific Humidity ($g/kg$) } |
2528 |
|
|
|
2529 |
|
|
\noindent |
2530 |
|
|
The diagnostic {\bf QAVE} is simply the time-averaged Specific Humidity over |
2531 |
|
|
the {\bf NQAVE} output frequency. This is contrasted to the instantaneous |
2532 |
|
|
Specific Humidity which is archived on the Prognostic Output data stream. |
2533 |
|
|
\[ |
2534 |
|
|
{\bf QAVE} = q(\lambda, \phi, level , t) |
2535 |
|
|
\] |
2536 |
|
|
\\ |
2537 |
|
|
|
2538 |
|
|
\noindent |
2539 |
|
|
{ \underline {PAVE} Time-Averaged Surface Pressure - PTOP ($mb$) } |
2540 |
|
|
|
2541 |
|
|
\noindent |
2542 |
|
|
The diagnostic {\bf PAVE} is simply the time-averaged Surface Pressure - PTOP over |
2543 |
|
|
the {\bf NPAVE} output frequency. This is contrasted to the instantaneous |
2544 |
|
|
Surface Pressure - PTOP which is archived on the Prognostic Output data stream. |
2545 |
|
|
\begin{eqnarray*} |
2546 |
|
|
{\bf PAVE} & = & \pi(\lambda, \phi, level , t) \\ |
2547 |
|
|
& = & p_s(\lambda, \phi, level , t) - p_T |
2548 |
|
|
\end{eqnarray*} |
2549 |
|
|
\\ |
2550 |
|
|
|
2551 |
|
|
|
2552 |
|
|
\noindent |
2553 |
|
|
{ \underline {QQAVE} Time-Averaged Turbulent Kinetic Energy $(m/sec)^2$ } |
2554 |
|
|
|
2555 |
|
|
\noindent |
2556 |
|
|
The diagnostic {\bf QQAVE} is simply the time-averaged prognostic Turbulent Kinetic Energy |
2557 |
|
|
produced by the GCM Turbulence parameterization over |
2558 |
|
|
the {\bf NQQAVE} output frequency. This is contrasted to the instantaneous |
2559 |
|
|
Turbulent Kinetic Energy which is archived on the Prognostic Output data stream. |
2560 |
|
|
\[ |
2561 |
|
|
{\bf QQAVE} = qq(\lambda, \phi, level , t) |
2562 |
|
|
\] |
2563 |
|
|
\\ |
2564 |
|
|
Note, {\bf QQAVE} is computed and stored at the ``mass-point'' locations on the staggered C-grid. |
2565 |
|
|
\\ |
2566 |
|
|
|
2567 |
|
|
\noindent |
2568 |
|
|
{ \underline {SWGCLR} Net downward clearsky Shortwave flux at the surface ($Watts/m^2$) } |
2569 |
|
|
|
2570 |
|
|
\noindent |
2571 |
|
|
\begin{eqnarray*} |
2572 |
|
|
{\bf SWGCLR} & = & F(clearsky)_{SW,Nrphys+1}^{Net} \\ |
2573 |
|
|
& = & F(clearsky)_{SW,Nrphys+1}^\downarrow - F(clearsky)_{SW,Nrphys+1}^\uparrow |
2574 |
|
|
\end{eqnarray*} |
2575 |
|
|
\noindent |
2576 |
|
|
\\ |
2577 |
|
|
where Nrphys+1 indicates the lowest model edge-level, or $p = p_{surf}$. |
2578 |
|
|
$F(clearsky){SW}^\downarrow$ is |
2579 |
|
|
the downward clearsky Shortwave flux and $F(clearsky)_{SW}^\uparrow$ is |
2580 |
|
|
the upward clearsky Shortwave flux. |
2581 |
|
|
\\ |
2582 |
|
|
|
2583 |
|
|
\noindent |
2584 |
|
|
{ \underline {DIABU} Total Diabatic Zonal U-Wind Tendency ($m/sec/day$) } |
2585 |
|
|
|
2586 |
|
|
\noindent |
2587 |
|
|
{\bf DIABU} is the total time-tendency of the Zonal U-Wind due to Diabatic processes |
2588 |
|
|
and the Analysis forcing. |
2589 |
|
|
\[ |
2590 |
|
|
{\bf DIABU} = \pp{u}{t}_{Moist} + \pp{u}{t}_{Turbulence} + \pp{u}{t}_{Analysis} |
2591 |
|
|
\] |
2592 |
|
|
\\ |
2593 |
|
|
|
2594 |
|
|
\noindent |
2595 |
|
|
{ \underline {DIABV} Total Diabatic Meridional V-Wind Tendency ($m/sec/day$) } |
2596 |
|
|
|
2597 |
|
|
\noindent |
2598 |
|
|
{\bf DIABV} is the total time-tendency of the Meridional V-Wind due to Diabatic processes |
2599 |
|
|
and the Analysis forcing. |
2600 |
|
|
\[ |
2601 |
|
|
{\bf DIABV} = \pp{v}{t}_{Moist} + \pp{v}{t}_{Turbulence} + \pp{v}{t}_{Analysis} |
2602 |
|
|
\] |
2603 |
|
|
\\ |
2604 |
|
|
|
2605 |
|
|
\noindent |
2606 |
|
|
{ \underline {DIABT} Total Diabatic Temperature Tendency ($deg/day$) } |
2607 |
|
|
|
2608 |
|
|
\noindent |
2609 |
|
|
{\bf DIABT} is the total time-tendency of Temperature due to Diabatic processes |
2610 |
|
|
and the Analysis forcing. |
2611 |
|
|
\begin{eqnarray*} |
2612 |
|
|
{\bf DIABT} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
2613 |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} + \pp{T}{t}_{Analysis} |
2614 |
|
|
\end{eqnarray*} |
2615 |
|
|
\\ |
2616 |
|
|
If we define the time-tendency of Temperature due to Diabatic processes as |
2617 |
|
|
\begin{eqnarray*} |
2618 |
|
|
\pp{T}{t}_{Diabatic} & = & \pp{T}{t}_{Moist Processes} + \pp{T}{t}_{Shortwave Radiation} \\ |
2619 |
|
|
& + & \pp{T}{t}_{Longwave Radiation} + \pp{T}{t}_{Turbulence} |
2620 |
|
|
\end{eqnarray*} |
2621 |
|
|
then, since there are no surface pressure changes due to Diabatic processes, we may write |
2622 |
|
|
\[ |
2623 |
|
|
\pp{T}{t}_{Diabatic} = {p^\kappa \over \pi }\pp{\pi \theta}{t}_{Diabatic} |
2624 |
|
|
\] |
2625 |
|
|
where $\theta = T/p^\kappa$. Thus, {\bf DIABT} may be written as |
2626 |
|
|
\[ |
2627 |
|
|
{\bf DIABT} = {p^\kappa \over \pi } \left( \pp{\pi \theta}{t}_{Diabatic} + \pp{\pi \theta}{t}_{Analysis} \right) |
2628 |
|
|
\] |
2629 |
|
|
\\ |
2630 |
|
|
|
2631 |
|
|
\noindent |
2632 |
|
|
{ \underline {DIABQ} Total Diabatic Specific Humidity Tendency ($g/kg/day$) } |
2633 |
|
|
|
2634 |
|
|
\noindent |
2635 |
|
|
{\bf DIABQ} is the total time-tendency of Specific Humidity due to Diabatic processes |
2636 |
|
|
and the Analysis forcing. |
2637 |
|
|
\[ |
2638 |
|
|
{\bf DIABQ} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} + \pp{q}{t}_{Analysis} |
2639 |
|
|
\] |
2640 |
|
|
If we define the time-tendency of Specific Humidity due to Diabatic processes as |
2641 |
|
|
\[ |
2642 |
|
|
\pp{q}{t}_{Diabatic} = \pp{q}{t}_{Moist Processes} + \pp{q}{t}_{Turbulence} |
2643 |
|
|
\] |
2644 |
|
|
then, since there are no surface pressure changes due to Diabatic processes, we may write |
2645 |
|
|
\[ |
2646 |
|
|
\pp{q}{t}_{Diabatic} = {1 \over \pi }\pp{\pi q}{t}_{Diabatic} |
2647 |
|
|
\] |
2648 |
|
|
Thus, {\bf DIABQ} may be written as |
2649 |
|
|
\[ |
2650 |
|
|
{\bf DIABQ} = {1 \over \pi } \left( \pp{\pi q}{t}_{Diabatic} + \pp{\pi q}{t}_{Analysis} \right) |
2651 |
|
|
\] |
2652 |
|
|
\\ |
2653 |
|
|
|
2654 |
|
|
\noindent |
2655 |
|
|
{ \underline {VINTUQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } |
2656 |
|
|
|
2657 |
|
|
\noindent |
2658 |
|
|
The vertically integrated moisture flux due to the zonal u-wind is obtained by integrating |
2659 |
|
|
$u q$ over the depth of the atmosphere at each model timestep, |
2660 |
|
|
and dividing by the total mass of the column. |
2661 |
|
|
\[ |
2662 |
|
|
{\bf VINTUQ} = \frac{ \int_{surf}^{top} u q \rho dz } { \int_{surf}^{top} \rho dz } |
2663 |
|
|
\] |
2664 |
|
|
Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have |
2665 |
|
|
\[ |
2666 |
|
|
{\bf VINTUQ} = { \int_0^1 u q dp } |
2667 |
|
|
\] |
2668 |
|
|
\\ |
2669 |
|
|
|
2670 |
|
|
|
2671 |
|
|
\noindent |
2672 |
|
|
{ \underline {VINTVQ} Vertically Integrated Moisture Flux ($m/sec \cdot g/kg$) } |
2673 |
|
|
|
2674 |
|
|
\noindent |
2675 |
|
|
The vertically integrated moisture flux due to the meridional v-wind is obtained by integrating |
2676 |
|
|
$v q$ over the depth of the atmosphere at each model timestep, |
2677 |
|
|
and dividing by the total mass of the column. |
2678 |
|
|
\[ |
2679 |
|
|
{\bf VINTVQ} = \frac{ \int_{surf}^{top} v q \rho dz } { \int_{surf}^{top} \rho dz } |
2680 |
|
|
\] |
2681 |
|
|
Using $\rho \delta z = -{\delta p \over g} = - {1 \over g} \delta p$, we have |
2682 |
|
|
\[ |
2683 |
|
|
{\bf VINTVQ} = { \int_0^1 v q dp } |
2684 |
|
|
\] |
2685 |
|
|
\\ |
2686 |
|
|
|
2687 |
|
|
|
2688 |
|
|
\noindent |
2689 |
|
|
{ \underline {VINTUT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } |
2690 |
|
|
|
2691 |
|
|
\noindent |
2692 |
|
|
The vertically integrated heat flux due to the zonal u-wind is obtained by integrating |
2693 |
|
|
$u T$ over the depth of the atmosphere at each model timestep, |
2694 |
|
|
and dividing by the total mass of the column. |
2695 |
|
|
\[ |
2696 |
|
|
{\bf VINTUT} = \frac{ \int_{surf}^{top} u T \rho dz } { \int_{surf}^{top} \rho dz } |
2697 |
|
|
\] |
2698 |
|
|
Or, |
2699 |
|
|
\[ |
2700 |
|
|
{\bf VINTUT} = { \int_0^1 u T dp } |
2701 |
|
|
\] |
2702 |
|
|
\\ |
2703 |
|
|
|
2704 |
|
|
\noindent |
2705 |
|
|
{ \underline {VINTVT} Vertically Integrated Heat Flux ($m/sec \cdot deg$) } |
2706 |
|
|
|
2707 |
|
|
\noindent |
2708 |
|
|
The vertically integrated heat flux due to the meridional v-wind is obtained by integrating |
2709 |
|
|
$v T$ over the depth of the atmosphere at each model timestep, |
2710 |
|
|
and dividing by the total mass of the column. |
2711 |
|
|
\[ |
2712 |
|
|
{\bf VINTVT} = \frac{ \int_{surf}^{top} v T \rho dz } { \int_{surf}^{top} \rho dz } |
2713 |
|
|
\] |
2714 |
|
|
Using $\rho \delta z = -{\delta p \over g} $, we have |
2715 |
|
|
\[ |
2716 |
|
|
{\bf VINTVT} = { \int_0^1 v T dp } |
2717 |
|
|
\] |
2718 |
|
|
\\ |
2719 |
|
|
|
2720 |
|
|
\noindent |
2721 |
|
|
{ \underline {CLDFRC} Total 2-Dimensional Cloud Fracton ($0-1$) } |
2722 |
|
|
|
2723 |
|
|
If we define the |
2724 |
|
|
time-averaged random and maximum overlapped cloudiness as CLRO and |
2725 |
|
|
CLMO respectively, then the probability of clear sky associated |
2726 |
|
|
with random overlapped clouds at any level is (1-CLRO) while the probability of |
2727 |
|
|
clear sky associated with maximum overlapped clouds at any level is (1-CLMO). |
2728 |
|
|
The total clear sky probability is given by (1-CLRO)*(1-CLMO), thus |
2729 |
|
|
the total cloud fraction at each level may be obtained by |
2730 |
|
|
1-(1-CLRO)*(1-CLMO). |
2731 |
|
|
|
2732 |
|
|
At any given level, we may define the clear line-of-site probability by |
2733 |
|
|
appropriately accounting for the maximum and random overlap |
2734 |
|
|
cloudiness. The clear line-of-site probability is defined to be |
2735 |
|
|
equal to the product of the clear line-of-site probabilities |
2736 |
|
|
associated with random and maximum overlap cloudiness. The clear |
2737 |
|
|
line-of-site probability $C(p,p^{\prime})$ associated with maximum overlap clouds, |
2738 |
|
|
from the current pressure $p$ |
2739 |
|
|
to the model top pressure, $p^{\prime} = p_{top}$, or the model surface pressure, $p^{\prime} = p_{surf}$, |
2740 |
|
|
is simply 1.0 minus the largest maximum overlap cloud value along the |
2741 |
|
|
line-of-site, ie. |
2742 |
|
|
|
2743 |
|
|
$$1-MAX_p^{p^{\prime}} \left( CLMO_p \right)$$ |
2744 |
|
|
|
2745 |
|
|
Thus, even in the time-averaged sense it is assumed that the |
2746 |
|
|
maximum overlap clouds are correlated in the vertical. The clear |
2747 |
|
|
line-of-site probability associated with random overlap clouds is |
2748 |
|
|
defined to be the product of the clear sky probabilities at each |
2749 |
|
|
level along the line-of-site, ie. |
2750 |
|
|
|
2751 |
|
|
$$\prod_{p}^{p^{\prime}} \left( 1-CLRO_p \right)$$ |
2752 |
|
|
|
2753 |
|
|
The total cloud fraction at a given level associated with a line- |
2754 |
|
|
of-site calculation is given by |
2755 |
|
|
|
2756 |
|
|
$$1-\left( 1-MAX_p^{p^{\prime}} \left[ CLMO_p \right] \right) |
2757 |
|
|
\prod_p^{p^{\prime}} \left( 1-CLRO_p \right)$$ |
2758 |
|
|
|
2759 |
|
|
|
2760 |
|
|
\noindent |
2761 |
|
|
The 2-dimensional net cloud fraction as seen from the top of the |
2762 |
|
|
atmosphere is given by |
2763 |
|
|
\[ |
2764 |
|
|
{\bf CLDFRC} = 1-\left( 1-MAX_{l=l_1}^{Nrphys} \left[ CLMO_l \right] \right) |
2765 |
|
|
\prod_{l=l_1}^{Nrphys} \left( 1-CLRO_l \right) |
2766 |
|
|
\] |
2767 |
|
|
\\ |
2768 |
|
|
For a complete description of cloud/radiative interactions, see Section \ref{sec:fizhi:radcloud}. |
2769 |
|
|
|
2770 |
|
|
|
2771 |
|
|
\noindent |
2772 |
|
|
{ \underline {QINT} Total Precipitable Water ($gm/cm^2$) } |
2773 |
|
|
|
2774 |
|
|
\noindent |
2775 |
|
|
The Total Precipitable Water is defined as the vertical integral of the specific humidity, |
2776 |
|
|
given by: |
2777 |
|
|
\begin{eqnarray*} |
2778 |
|
|
{\bf QINT} & = & \int_{surf}^{top} \rho q dz \\ |
2779 |
|
|
& = & {\pi \over g} \int_0^1 q dp |
2780 |
|
|
\end{eqnarray*} |
2781 |
|
|
where we have used the hydrostatic relation |
2782 |
|
|
$\rho \delta z = -{\delta p \over g} $. |
2783 |
|
|
\\ |
2784 |
|
|
|
2785 |
|
|
|
2786 |
|
|
\noindent |
2787 |
|
|
{ \underline {U2M} Zonal U-Wind at 2 Meter Depth ($m/sec$) } |
2788 |
|
|
|
2789 |
|
|
\noindent |
2790 |
|
|
The u-wind at the 2-meter depth is determined from the similarity theory: |
2791 |
|
|
\[ |
2792 |
|
|
{\bf U2M} = {u_* \over k} \psi_{m_{2m}} {u_{sl} \over {W_s}} = |
2793 |
|
|
{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}u_{sl} |
2794 |
|
|
\] |
2795 |
|
|
|
2796 |
|
|
\noindent |
2797 |
|
|
where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript |
2798 |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
2799 |
|
|
is above two meters, ${\bf U2M}$ is undefined. |
2800 |
|
|
\\ |
2801 |
|
|
|
2802 |
|
|
\noindent |
2803 |
|
|
{ \underline {V2M} Meridional V-Wind at 2 Meter Depth ($m/sec$) } |
2804 |
|
|
|
2805 |
|
|
\noindent |
2806 |
|
|
The v-wind at the 2-meter depth is a determined from the similarity theory: |
2807 |
|
|
\[ |
2808 |
|
|
{\bf V2M} = {u_* \over k} \psi_{m_{2m}} {v_{sl} \over {W_s}} = |
2809 |
|
|
{ \psi_{m_{2m}} \over {\psi_{m_{sl}} }}v_{sl} |
2810 |
|
|
\] |
2811 |
|
|
|
2812 |
|
|
\noindent |
2813 |
|
|
where $\psi_m(2m)$ is the non-dimensional wind shear at two meters, and the subscript |
2814 |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
2815 |
|
|
is above two meters, ${\bf V2M}$ is undefined. |
2816 |
|
|
\\ |
2817 |
|
|
|
2818 |
|
|
\noindent |
2819 |
|
|
{ \underline {T2M} Temperature at 2 Meter Depth ($deg \hspace{.1cm} K$) } |
2820 |
|
|
|
2821 |
|
|
\noindent |
2822 |
|
|
The temperature at the 2-meter depth is a determined from the similarity theory: |
2823 |
|
|
\[ |
2824 |
|
|
{\bf T2M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{2m}}+\psi_g}) + \theta_{surf} ) = |
2825 |
|
|
P^{\kappa}(\theta_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
2826 |
|
|
(\theta_{sl} - \theta_{surf})) |
2827 |
|
|
\] |
2828 |
|
|
where: |
2829 |
|
|
\[ |
2830 |
|
|
\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } |
2831 |
|
|
\] |
2832 |
|
|
|
2833 |
|
|
\noindent |
2834 |
|
|
where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
2835 |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
2836 |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
2837 |
|
|
is above two meters, ${\bf T2M}$ is undefined. |
2838 |
|
|
\\ |
2839 |
|
|
|
2840 |
|
|
\noindent |
2841 |
|
|
{ \underline {Q2M} Specific Humidity at 2 Meter Depth ($g/kg$) } |
2842 |
|
|
|
2843 |
|
|
\noindent |
2844 |
|
|
The specific humidity at the 2-meter depth is determined from the similarity theory: |
2845 |
|
|
\[ |
2846 |
|
|
{\bf Q2M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{2m}}+\psi_g}) + q_{surf} ) = |
2847 |
|
|
P^{\kappa}(q_{surf} + { {\psi_{h_{2m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
2848 |
|
|
(q_{sl} - q_{surf})) |
2849 |
|
|
\] |
2850 |
|
|
where: |
2851 |
|
|
\[ |
2852 |
|
|
q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } |
2853 |
|
|
\] |
2854 |
|
|
|
2855 |
|
|
\noindent |
2856 |
|
|
where $\psi_h(2m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
2857 |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
2858 |
|
|
$sl$ refers to the height of the top of the surface layer. If the roughness height |
2859 |
|
|
is above two meters, ${\bf Q2M}$ is undefined. |
2860 |
|
|
\\ |
2861 |
|
|
|
2862 |
|
|
\noindent |
2863 |
|
|
{ \underline {U10M} Zonal U-Wind at 10 Meter Depth ($m/sec$) } |
2864 |
|
|
|
2865 |
|
|
\noindent |
2866 |
|
|
The u-wind at the 10-meter depth is an interpolation between the surface wind |
2867 |
|
|
and the model lowest level wind using the ratio of the non-dimensional wind shear |
2868 |
|
|
at the two levels: |
2869 |
|
|
\[ |
2870 |
|
|
{\bf U10M} = {u_* \over k} \psi_{m_{10m}} {u_{sl} \over {W_s}} = |
2871 |
|
|
{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}u_{sl} |
2872 |
|
|
\] |
2873 |
|
|
|
2874 |
|
|
\noindent |
2875 |
|
|
where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript |
2876 |
|
|
$sl$ refers to the height of the top of the surface layer. |
2877 |
|
|
\\ |
2878 |
|
|
|
2879 |
|
|
\noindent |
2880 |
|
|
{ \underline {V10M} Meridional V-Wind at 10 Meter Depth ($m/sec$) } |
2881 |
|
|
|
2882 |
|
|
\noindent |
2883 |
|
|
The v-wind at the 10-meter depth is an interpolation between the surface wind |
2884 |
|
|
and the model lowest level wind using the ratio of the non-dimensional wind shear |
2885 |
|
|
at the two levels: |
2886 |
|
|
\[ |
2887 |
|
|
{\bf V10M} = {u_* \over k} \psi_{m_{10m}} {v_{sl} \over {W_s}} = |
2888 |
|
|
{ \psi_{m_{10m}} \over {\psi_{m_{sl}} }}v_{sl} |
2889 |
|
|
\] |
2890 |
|
|
|
2891 |
|
|
\noindent |
2892 |
|
|
where $\psi_m(10m)$ is the non-dimensional wind shear at ten meters, and the subscript |
2893 |
|
|
$sl$ refers to the height of the top of the surface layer. |
2894 |
|
|
\\ |
2895 |
|
|
|
2896 |
|
|
\noindent |
2897 |
|
|
{ \underline {T10M} Temperature at 10 Meter Depth ($deg \hspace{.1cm} K$) } |
2898 |
|
|
|
2899 |
|
|
\noindent |
2900 |
|
|
The temperature at the 10-meter depth is an interpolation between the surface potential |
2901 |
|
|
temperature and the model lowest level potential temperature using the ratio of the |
2902 |
|
|
non-dimensional temperature gradient at the two levels: |
2903 |
|
|
\[ |
2904 |
|
|
{\bf T10M} = P^{\kappa} ({\theta* \over k} ({\psi_{h_{10m}}+\psi_g}) + \theta_{surf} ) = |
2905 |
|
|
P^{\kappa}(\theta_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
2906 |
|
|
(\theta_{sl} - \theta_{surf})) |
2907 |
|
|
\] |
2908 |
|
|
where: |
2909 |
|
|
\[ |
2910 |
|
|
\theta_* = - { (\overline{w^{\prime}\theta^{\prime}}) \over {u_*} } |
2911 |
|
|
\] |
2912 |
|
|
|
2913 |
|
|
\noindent |
2914 |
|
|
where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
2915 |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
2916 |
|
|
$sl$ refers to the height of the top of the surface layer. |
2917 |
|
|
\\ |
2918 |
|
|
|
2919 |
|
|
\noindent |
2920 |
|
|
{ \underline {Q10M} Specific Humidity at 10 Meter Depth ($g/kg$) } |
2921 |
|
|
|
2922 |
|
|
\noindent |
2923 |
|
|
The specific humidity at the 10-meter depth is an interpolation between the surface specific |
2924 |
|
|
humidity and the model lowest level specific humidity using the ratio of the |
2925 |
|
|
non-dimensional temperature gradient at the two levels: |
2926 |
|
|
\[ |
2927 |
|
|
{\bf Q10M} = P^{\kappa} ({q_* \over k} ({\psi_{h_{10m}}+\psi_g}) + q_{surf} ) = |
2928 |
|
|
P^{\kappa}(q_{surf} + { {\psi_{h_{10m}}+\psi_g} \over {{\psi_{h_{sl}}+\psi_g}} } |
2929 |
|
|
(q_{sl} - q_{surf})) |
2930 |
|
|
\] |
2931 |
|
|
where: |
2932 |
|
|
\[ |
2933 |
|
|
q_* = - { (\overline{w^{\prime}q^{\prime}}) \over {u_*} } |
2934 |
|
|
\] |
2935 |
|
|
|
2936 |
|
|
\noindent |
2937 |
|
|
where $\psi_h(10m)$ is the non-dimensional temperature gradient at two meters, $\psi_g$ is |
2938 |
|
|
the non-dimensional temperature gradient in the viscous sublayer, and the subscript |
2939 |
|
|
$sl$ refers to the height of the top of the surface layer. |
2940 |
|
|
\\ |
2941 |
|
|
|
2942 |
|
|
\noindent |
2943 |
|
|
{ \underline {DTRAIN} Cloud Detrainment Mass Flux ($kg/m^2$) } |
2944 |
|
|
|
2945 |
|
|
The amount of cloud mass moved per RAS timestep at the cloud detrainment level is written: |
2946 |
|
|
\[ |
2947 |
|
|
{\bf DTRAIN} = \eta_{r_D}m_B |
2948 |
|
|
\] |
2949 |
|
|
\noindent |
2950 |
|
|
where $r_D$ is the detrainment level, |
2951 |
|
|
$m_B$ is the cloud base mass flux, and $\eta$ |
2952 |
|
|
is the entrainment, defined in Section \ref{sec:fizhi:mc}. |
2953 |
|
|
\\ |
2954 |
|
|
|
2955 |
|
|
\noindent |
2956 |
|
|
{ \underline {QFILL} Filling of negative Specific Humidity ($g/kg/day$) } |
2957 |
|
|
|
2958 |
|
|
\noindent |
2959 |
|
|
Due to computational errors associated with the numerical scheme used for |
2960 |
|
|
the advection of moisture, negative values of specific humidity may be generated. The |
2961 |
|
|
specific humidity is checked for negative values after every dynamics timestep. If negative |
2962 |
|
|
values have been produced, a filling algorithm is invoked which redistributes moisture from |
2963 |
|
|
below. Diagnostic {\bf QFILL} is equal to the net filling needed |
2964 |
|
|
to eliminate negative specific humidity, scaled to a per-day rate: |
2965 |
|
|
\[ |
2966 |
|
|
{\bf QFILL} = q^{n+1}_{final} - q^{n+1}_{initial} |
2967 |
|
|
\] |
2968 |
|
|
where |
2969 |
|
|
\[ |
2970 |
|
|
q^{n+1} = (\pi q)^{n+1} / \pi^{n+1} |
2971 |
|
|
\] |
2972 |
|
|
|
2973 |
|
|
|
2974 |
molod |
1.9 |
\subsubsection{Key subroutines, parameters and files} |
2975 |
molod |
1.6 |
|
2976 |
molod |
1.9 |
\subsubsection{Dos and donts} |
2977 |
molod |
1.6 |
|
2978 |
molod |
1.9 |
\subsubsection{Fizhi Reference} |